%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % % Bibliography-database for the SYNODE Project % % % % Topic: Symplectic Integration % % % % Version: % % '$Id: hamilt.bib,v 1.45 2002/03/23 15:53:39 arnema Exp $' % % % % Construction of the cite key: % % All letters are in lower case. The key starts with the last % % name of the first author followed by two numbers identifying % % the publication year. The key ends with the first letter of % % the first three words in the title of the paper. For most % % papers this key is unique. However, if the first three words % % are equal, we use the first three letters followed by a % % positive number (e.g. 1, 2, 3,...). If the title consists of % % less than three words, we still use only the first letter of % % each word. % % % % If you do not find the correct key, you should just search through % % the file looking for one of the authors. There are a number of ways % % to do this, use e.g. your favorite text editor or the UNIX tools % % 'grep'} or 'less'. % % % % Disclaimer: The makers of this bibliography will not accept % % responsibility for any consequences of errors and % % misprints. % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% @string{ an = "Acta Numerica" } @string{ am = "Advances in Mathematics" } @string{ annalsnm = "Annals of Numer. Math." } @string{ amc = "Applied Mathematics and Computation" } @string{ aml = "Appl. Math. Lett." } @string{ anm = "Appl. Numer. Math." } @string{ arma = "Arch. Rat. Mech. Anal" } @string{ aj = "Astron. J." } @string{ bioj = "Biophys. J." } @string{ bit = "BIT" } @string{ bhms = "Bull. Hellenic Math. Soc." } @string{ cm = "Celest. Mech." } @string{ cmda = "Celest. Mech. and Dyn. Astro." } @string{ cmwa = "Comp. \& Math. with Applic." } @string{ cpam = "Comm. Pure and Appl. Math." } @string{ comp = "Computing" } @string{ cma = "Computers Math. Applic." } @string{ cmp = "Communications in Mathematical Physics" } @string{ cmame = "Comput. Methods Appl. Mech. Engrg." } @string{ cp = "Chemical Physics" } @string{ cpl = "Chemical Physics Letters" } @string{ cpc = "Comput. Phys. Comm." } @string{ etna = "Electronic Transactions on Numerical Analysis" } @string{ fic = "Fields Inst. Com." } @string{ ieeetac = "IEEE Trans. Automatic Control" } @string{ ieeetns = "IEEE Trans. Nucl. Sci." } @string{ imajna = "IMA J. Numer. Anal." } @string{ ijcm = "Internat. J. Comput. Math." } @string{ ilnme = "Internat. J. Numer. Methods Engrg." } @string{ ijqc = "Int. J. of Quant. Chem." } @string{ ijss = "Internat. J. Solids Structures" } @string{ ijqc = "Int. J. Quant. Chem." } @string{ jamm = "J. Appl. Math. Mech." } @string{ jcics = "J. Chem. Inf. Comp. Sci." } @string{ jcam = "J. Comput. Appl. Math" } @string{ jcc = "J. Comput. Chem." } @string{ jcm = "J. Comput. Math." } @string{ jde = "J. Differential Equations" } @string{ jmsec = "J. of Math. Systems, Estimation, and Control" } @string{ jnp = "J. Nath. Phys." } @string{ jnmca = "J. Num. Method and Comp. Appl." } @string{ jcics = "J. of Chem. Inf. and Comp. Sci." } @string{ jchemp = "J. Chem. Phys." } @string{ jcp = "J. of Comp. Phys." } @string{ jmp = "J. of Math. Phys." } @string{ jns = "J. Nonlinear. Sci." } @string{ jpa = "J. Phys. A" } @string{ jpamg = "J. Phys. A: Math. Gen." } @string{ jpc = "J. Phys. Chem." } @string{ jsp = "J. Stat. Phys." } @string{ jsc = "Journal of Symbolic Computation" } @string{ lmp = "Letters in Mathematical Physics" } @string{ ma = "Math. Appl." } @string{ mac = "Mathematics and Computers in Simultation" } @string{ mc = "Math. Comp." } @string{ mcis = "Mathematics and Computers in Simulation" } @string{ mmos = "Mathematical Modelling of Systems" } @string{ molsim = "Mol. Sim." } @string{ mwr = "Monthly Weather Rev." } @string{ nm = "Numer. Math." } @string{ nonlin = "Nonlinearity" } @string{ npb = "Nuclear Physics B" } @string{ prd = "Physical Review D" } @string{ pa = "Physica A" } @string{ pd = "Physica D" } @string{ pl = "Phys. Lett." } @string{ pla = "Physics Letters A" } @string{ pre = "Physical Review E" } @string{ prl = "Physical Review Letters" } @string{ prsla = "Proc. R. Soc. Lond. A" } @string{ pns = "Progr. Natur. Sci." } @string{ pibmb = "Progress in Biophy. \& Mol. Biol." } @string{ qm = "Quaestiones Mathematicae" } @string{ rmp = "Reports on Mathematical Physics" } @string{ sijam = "SIAM J. Appl. Math." } @string{ sijna = "SIAM J. Numer. Anal." } @string{ sisc = "SIAM J. Sci. Comput." } @string{ sir = "SIAM Review" } @string{ zamp = "Z. Angew. Math. Phys." } %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% @Article{abdullaev, author = {S. S. Abdullaev}, title = {A New Integration Method of {H}amiltonian Systems by Symplectic Maps}, journal = jpamg, year = 1999, volume = 32, number = 15, pages = {2745--2766} } @Article{abdullaev02thj, author = {S. S. Abdullaev}, title = {The {H}amilton-{J}acobi Method and {H}amiltonian Maps}, journal = jpamg, year = 2002, volume = 35, number = 12, pages = {2811--2832} } @Article{abia93prk, author = {L. Abia and J.M. Sanz{--}Serna}, title = {Partitioned {R}unge-{K}utta methods for separable {H}amiltonian problems}, journal = mc, year = 1993, volume = 60, pages = {617--634} } @Article{akishin97ahn, author = {P. G. Akishin and I. V. Puzynin and S. I. Vinitsky}, title = {A hybrid numerical method for analysis of dynamics of classical {H}amiltonian systems}, journal = cma, year = 1997, volume = 34, pages = {45--73} } @InProceedings{alvarez93tsp, author = {M. Alvarez and J. Delgado}, title = {{T}he spring-pendelum system}, booktitle = {{H}amiltonian {S}ystems and {C}elestical {M}echanics}, editor = {E. A. Lacomba and J. Llibre}, year = 1993, publisher = {{W}orld {S}cientific {P}ublishing}, pages = {1--14} } @Book{anosov88dsi, author = {D.V. Anosov and V.I. Arnold}, title = {{D}ynamical {S}ystems {I}}, publisher = {Springer, Berlin}, year = 1988 } @Article{araujo97smb, author = {A. L. Ara{\'u}jo and A. Murua and J. M. Sanz-Serna}, title = {{S}ymplectic {M}ethods {B}ased on {D}ecompositions}, journal = sijna, year = 1997, volume = 34, number = 5, pages = {1926--1947} } @Book{arnold89mmo, author = {V.I. Arnold}, title = {{M}athematical {M}ethods of {C}lassical {M}echanics}, publisher = {Springer, New York}, year = 1988, edition = {2nd} } @TechReport{ascher97osd, author = {U. Ascher and S. Reich}, title = {On some difficulties in integrating highly oscillatory {H}amiltonian system}, institution = {Department of Computer Science, University of British Columbia}, year = 1997 } @Unpublished{ascher97tms, author = {U. M. Ascher and S. Reich}, title = {{T}he midpoint scheme and variants for {H}amiltonian systems: advantages and pitfalls}, note = {To appear} } @TechReport{aubry97psr, author = {A. Aubry and P. Chartier}, title = {{P}seudo-symplectic {R}unge-{K}utta methods}, institution = {{IRISA}}, year = 1997 } @Article{aubry98ano, author = {A. Aubry and P. Chartier}, title = {{A} {N}ote on {P}seudo-{S}ymplectic {R}unge-{K}utta {M}ethods}, journal = bit, year = 1998, volume = 38, number = 4, pages = {802--806} } @Article{auerbach91ltb, author = {S. P. Auerbach and A. Friedman}, title = {{L}ong-time behavior of numerically computed orbits: {S}mall and intermediate timestep analysis of one-dimensional systems}, journal = jcp, year = 1991, volume = 93, pages = {189--223} } @Article{barth95smf, author = {E. Barth and B. Leimkuhler}, title = {{S}ymplectic {M}ethods for {C}onservative {M}ultibody {S}ystems}, journal = fic, year = 1995, note = {To appear} } @Unpublished{barth96ase, author = {E. Barth and B. Leimkuhler}, title = {{A} semi-explicit, variable-step size integrator for constrained dynamics}, note = {To appear}, year = 1996 } @InCollection{barth96smf, author = {E. Barth and B. Leimkuhler}, title = {{S}ymplectic {M}ethods for {C}onservative {M}ultibody {S}ystems}, booktitle = {{I}ntegration {A}lgorithms and {C}lassical {M}echanics}, publisher = {American Mathematical Society}, year = 1996, editor = {J. E. Mardsen and G. W. Patrick and W. F. Shadwick}, pages = {25--44} } @Article{benzel93eco, author = {S. Benzel and Ge Zhong and C. Scovel}, title = {{E}lementary construction of higher order {L}ie-{P}oisson integrators}, journal = pla, year = 1993, volume = 174, pages = {229--232} } @InProceedings{beyn91nmf, author = {W.J. Beyn}, title = {{N}umerical methods for dynamical systems}, booktitle = {{A}dvances in {N}umerical {A}nalysis}, editor = {W. Light}, volume = {{I}}, year = 1991, publisher = {Clarendon Press, Oxford}, pages = {175--236} } @Article{biesiadecki93dom, author = {{J}.{J}. {B}iesiadecki and {R}.{D}. Skeel}, title = {{D}angers of multiple-time-step methods}, journal = jcp, year = 1993, volume = 109, pages = {318--328} } @Book{brenan89nso, author = {K.E. Brenan and S.L. Campbell and L.R. Petzold}, title = {{N}umerical {S}olution of {I}nitial-{V}alue {P}roblems in {D}ifferential-{A}lgebraic {E}quations}, publisher = {North-Holland, New York}, year = 1989 } @Article{brouzet96tdo, author = {R. Brouzet and R. Caboz and J. Rabenivo and V. Ravonson}, title = {{T}wo-degrees of freedom quasi {B}i-{H}amiltonian systems}, journal = pla, year = 1996, volume = 29, pages = {2069--2076} } @Article{burrage79scf, author = {K. Burrage and J.C. Butcher}, title = {{S}tability criteria for implicit {R}unge-{K}utta methods}, journal = sijna, year = 1979, volume = 16, pages = {46--57} } @Article{butcher64irk, author = {J.C. Butcher}, title = {{I}mplicit {R}unge-{K}utta {P}rocesses}, journal = mc, year = 1964, volume = 18, pages = {50--64} } @Book{butcher87tna, author = {J.C. Butcher}, title = {{T}he {N}umerical {A}nalysis of {O}rdinary {D}ifferential {E}quations}, publisher = {John Wiley, Chichester}, year = 1987 } @Article{caboz91bhs, author = {R. Caboz and V. Ravonson and L. Gavrilov}, title = {{B}i-{H}amiltonian structure of an integrable {H}{\'e}non-{H}eiles system}, journal = jpa, year = 1991, volume = 24, pages = {L523--L525} } @Article{calvo02hos, author = {M. P. Calvo}, title = {High Order Starting Iterates for Implicit {R}unge--{K}utta Methods: an Improvement for Variable-Step Symplectic Integrators}, journal = imajna, year = 2002, volume = 22, number = 1, pages = {153--166} } @InProceedings{calvo91cos, author = {M.P. Calvo}, title = {{C}haracterization of {S}ymplectic {R}unge-{K}utta-{N}ystr{\"o}m {M}ethods}, booktitle = {Proceedings of the XII Congress on Differential Equations and Applications}, year = 1991, publisher = {University of Oviedo, Oviedo}, pages = {111--115} } @PhdThesis{calvo92mrk, author = {M.P. Calvo}, title = {{M}{\'e}todos {R}unge-{K}utta-{N}ystr{\"{o}}m {S}impl{\'{e}}cticos}, school = {Universidad de Valladolid}, year = 1992 } @Article{calvo92ocf, author = {M.P. Calvo and J.M. Sanz{--}Serna}, title = {{O}rder conditions for canonical {R}unge-{K}utta-{N}ystr{\"o}m methods}, journal = bit, year = 1992, volume = 32, pages = {131--142} } @InProceedings{calvo92vsf, author = {M.P. Calvo and J.M. Sanz{--}Serna}, title = {{V}ariable steps for symplectic integrators}, booktitle = {Numerical Analysis, 1991}, editor = {D.F. Griffiths and G.A. Watson}, year = 1992, publisher = {Longman, London}, pages = {34--48} } @Article{calvo93hos, author = {M.P. Calvo and J.M. Sanz{--}Serna}, title = {{H}igh-order symplectic {R}unge-{K}utta-{N}ystr{\"{o}}m methods}, journal = sisc, year = 1993, volume = 114, pages = {1237--1252} } @InProceedings{calvo93rff, author = {M.P. Calvo and J.M. Sanz{--}Serna}, title = {{R}easons for failure. {T}he integration of the two-body problem with a symplectic {R}unge-{K}utta-{N}ystr{\"o}m code with stepchanging facilities}, booktitle = {Equadiff 91}, editor = {C. Perell{\'{o}} and C. Simo and J. Sola-Morales}, year = 1993, publisher = {World Scientific, Singapore}, pages = {34--48} } @Article{calvo93tdo, author = {M.P. Calvo and J.M. Sanz{--}Serna}, title = {The development of variable-step symplectic integrators with application to the two-body problem}, journal = sisc, year = 1993, volume = 14, pages = {936--952} } @Article{calvo94cbs, author = {M.P. Calvo and J.M. Sanz{--}Serna}, title = {{C}anonical {B}-{S}eries}, journal = nm, year = 1994, volume = 67, pages = {161--175} } @InProceedings{calvo94mef, author = {M. P. Calvo and A. Murua and J. M. Sanz-Serna}, title = {{M}odified {E}quations for {ODE}'s}, booktitle = {{C}haotic {N}umerics}, number = 172, series = {{C}ontemporary {M}athematics}, year = 1994, publisher = {{A}merican {M}athematical {S}ociety}, pages = {1--30} } @Article{calvo95alt, author = {M.P. Calvo and E. Hairer}, title = {{A}ccurate {L}ong-{T}erm {I}ntegration of {D}ynamical {S}ystems}, journal = nm, year = 1995, volume = 18, pages = {95--105} } @Article{calvo95fri, author = {M.P. Calvo and E. Hairer}, title = {{F}urther {R}eduction in the {N}umber of {I}ndependent {O}rder {C}onditions for {S}ymplectic, {E}xplicit {P}artitioned {R}unge-{K}utta and {R}unge-{K}utta-{N}ystr{\"o}m {M}ethods}, journal = anm, year = 1995, volume = 18, pages = {107--114} } @TechReport{calvo95rkm, author = {M. P. Calvo and A. Iserles and A. Zanna}, title = {{R}unge-{K}utta methods on manifolds}, institution = {{U}niversity of {C}ambridge}, year = 1995, number = {{DAMPT} 1995/{NA}7} } @Article{candy91asi, author = {J. Candy and W. Rozmus}, title = {A symplectic integration algorithm for separable {H}amiltonian functions}, journal = jcp, year = 1991, volume = 92, pages = {230--256} } @Article{cano97egi, author = {B. Cano and J. M. Sanz-Serna}, title = {{E}rror {G}rowth in the {N}umerical {I}ntegration of {P}eriodic {O}rbots, with {A}pplication to {H}amiltonian and {R}eversible {S}ystems}, journal = sijna, year = 1997, volume = 34, number = 4 } @Article{casas96ffa, author = {F. Casas}, title = {{F}er's {F}actorization as a {S}ymplectic {I}ntegrator}, journal = nm, year = 1996, volume = 74, number = 3, pages = {283--303} } @Article{chan90osr, author = {R. P. K. Chan}, title = {{O}n symmetric {R}unge-{K}utta methods of high order}, journal = comp, year = 1990, volume = 45, pages = {301--309} } @Article{channel91ifl, author = {P. J. Channel and J. S. Scovel}, title = {{I}ntegrators for {L}ie-{P}oisson dynamical systems}, journal = pd, year = 1991, volume = 50, pages = {80--88} } @TechReport{channell83sia, author = {P. J. Channel}, title = {Symplectic integration algorithms}, institution = {Los Alamos National Laboratory}, year = 1983, number = {AT-6:ATN 83--9} } @Article{channell90sio, author = {P.J. Channell and C. Scovel}, title = {Symplectic integration of {H}amiltonian systems}, journal = nonlin, year = 1990, volume = 3, pages = {231--259} } @InCollection{channell96ait, author = {P. J. Channell and F. R. Neri}, title = {{A}n {I}ntroduction to {S}ymplectic {I}ntegrators}, booktitle = {{I}ntegration {A}lgorithms and {C}lassical {M}echanics}, publisher = {American Mathematical Society}, year = 1996, editor = {J. E. Mardsen and G. W. Patrick and W. F. Shadwick}, pages = {45--58} } @Article{chatterjee96dsa, author = {R. Chatterjee}, title = {{D}ynamical symmetries and {N}ambu mechanics}, journal = lmp, year = 1996, volume = 36, pages = {117--126} } @Article{chin97sif, author = {S. A. Chin}, title = {{S}ymplectic integrators from composite operator factorization}, journal = pla, year = 1997, volume = 226, pages = {344--348} } @Article{cooper87sor, author = {G. J. Cooper}, title = {{S}tability of {R}unge-{K}utta {M}ethods for {T}rajectory {P}roblems}, journal = imajna, year = 1987, volume = 7, pages = {1--13} } @Article{cooper90asf, author = {{G}.{J}. {C}ooper and {R}. {V}ignesvaran}, title = {A scheme for the implementation of implicit {R}unge-{K}utta methods}, journal = comp, year = 1990, volume = 45, pages = {321--332} } @Article{cronstrom95mhs, author = {C. Cronstr{\"o}m and M. Noga}, title = {{M}ulti-{H}amiltonian structure of the {L}otka-{V}olterra and quantum {V}olterra models}, journal = npb, year = 1995, volume = 445, pages = {501--515} } @Article{crouzeix79slb, author = {{M}. {C}rouzeix}, title = {Sur la {B}-stabilit{\'{e}} des m{\'{e}}thodes de {R}unge-{K}utta}, journal = nm, year = 1979, volume = 32, pages = {75--82} } @InProceedings{dahlquist75eaf, author = {{G}. {D}ahlquist}, title = {Error analysis for a class of methods for stiff nonlinear initial value problems}, booktitle = {Numerical Analysis, Dundee, 1975}, editor = {G.A. Watson}, year = 1975, publisher = {Springer, Berlin}, pages = {60--74} } @Book{dekker84sor, author = {{K}. {D}ekker and {J}.{G}. {V}erwer}, title = {Stability of {R}unge-{K}utta {M}ethods for {S}tiff {I}nitial {V}alue {P}roblems}, publisher = {North-Holland, Amsterdam}, year = 1984 } @Article{dormand87for, author = {J.R. Dormand and M.E.A. El-Mikkawy and P.J. Prince}, title = {Families of {R}unge-{K}utta-{N}ystr{\"{o}}m formulae}, journal = imajna, year = 1987, volume = 7, pages = {235--250} } @Article{dormand87hoe, author = {J.R. Dormand and M.E.A. El-Mikkawy and P.J. Prince}, title = {High-order embedded {R}unge-{K}utta-{N}ystr{\"{o}}m formulae}, journal = imajna, year = 1987, volume = 11, pages = 297 } @Article{dormand89prk, author = {{J}. {R}. {D}ormand and {P}. {J}. {P}rince}, title = {Practical {R}unge-{K}utta processes}, journal = sisc, year = 1989, volume = 10, pages = {977--989} } @Article{dragt76lsa, author = {{A}.{J}. {D}ragt and {J}.{M}. {F}inn}, title = {Lie series and invariant functions for analytic symplectic maps}, journal = jnp, year = 1976, volume = 17, pages = {2215--2227} } @Article{dragt83con, author = {{A}.{J}. {D}ragt and {E}. {F}orest}, title = {{C}omputation of {N}onlinear {B}ehavior of {H}amiltonian {S}ystems using {L}ie {A}lgebraic {M}ethods}, journal = jmp, year = 1983, volume = 24, number = 12, pages = {2734--2744} } @InCollection{dragt96sma, author = {A. J. Dragt and D. T. Abell}, title = {{S}ymplectic {M}aps and {C}omputation of {O}rbits in {P}article {A}ccelerators}, booktitle = {{I}ntegration {A}lgorithms and {C}lassical {M}echanics}, publisher = {American Mathematical Society}, year = 1996, editor = {J. E. Mardsen and G. W. Patrick and W. F. Shadwick}, pages = {59--86} } @TechReport{dullweber97shm, author = {A. Dullweber and B. Leimkuhler and R. I. McLachlan}, title = {{S}plit-{H}amiltonian {M}ethods for {R}igid {B}ody {M}olecular {D}ynamics}, institution = {Department of Applied Mathematics and Theoretical Physics, University of Cambridge}, year = 1997, number = {1997/{NA}11} } @PhdThesis{eikelder84can, author = {H. M. M. Ten Eikelder}, title = {{C}anonical and {N}on-canonical {S}ymmetries for {H}amiltonian {S}ystems}, school = {Technical University of Eindhoven}, year = 1984 } @Article{eirola92coi, author = {{T}. {E}irola and {J}.{M}. {S}anz-{S}erna}, title = {Conservation of integrals and symplectic structure in the integration of differential equations by multistep methods}, journal = nm, year = 1992, volume = 61, pages = {281--290} } @Article{eirola93aob, author = {{T}. {E}irola}, title = {Aspects of backward error analysus of numerical {ODE}s}, journal = jcam, year = 1993, volume = 45, pages = {65--73} } @Article{eirola95moq, author = {{T}. Eirola}, title = {{M}onotonicity of {Q}uadratic {F}orms with {S}ymplectic {R}unge-{K}utta {M}ethods}, journal = anm, year = 1995, volume = 17, number = 3, pages = {293--298} } @Article{ergenc96rkc, author = {T. Ergen{\c{c}} and B. Karas{\"o}zen}, title = {{R}unge-{K}utta {C}ollocation {M}ethods for {R}igid {B}ody {L}ie-{P}oisson {E}quations}, journal = ijcm, year = 1996, volume = 62, pages = {63--71} } @Article{estep95tro, author = {D. J. Estep and A. M. Stuart}, title = {{T}he {R}ate of {E}rror {G}rowth in {H}amiltonian-{C}onserving {I}ntegrators}, journal = zamp, year = 1995, volume = 46, number = 3, pages = {407--418} } @InProceedings{feng83cie, author = {{K}. {F}eng and {D}.{H}. {Y}u}, title = {{C}anonical {I}ntegral {E}quations of {E}lliptic {B}oundary {V}alue {P}roblems and their {N}umerical {S}olutions}, booktitle = {Proceedings of the China-France symposium on finite element methods (Beijing, 1982)}, year = 1983, publisher = {Science Press, Beijing}, pages = {211--252} } @InProceedings{feng85ods, author = {{K}. {F}eng}, title = {On difference schemes and symplectic geometry}, booktitle = {Proceedings of the 1984 {B}eijing {S}ymposium on {D}ifferential {G}eometry and {D}ifferential {E}quations}, editor = {K. Feng}, year = 1985, publisher = {Science {P}ress, Beijing}, pages = {42--58} } @InProceedings{feng86cds, author = {{K}. {F}eng}, title = {{C}anonical {D}ifference {S}chemes for {H}amiltonian {C}anonical {D}ifferential {E}quations}, booktitle = {International Workshop on Applied Differential Equations (Beijing, 1985)}, year = 1986, publisher = {World Sci. Publishing, Singapore}, pages = {59--73} } @Article{feng86dsf, author = {{K}. {F}eng}, title = {Difference schemes for {H}amiltonian formalism and symplectic geometry}, journal = jcm, year = 1986, volume = 4, pages = {279--289} } @InProceedings{feng86sga, author = {{K}. {F}eng}, title = {Symplectic geometry and numerical methods in fluid dynamics}, booktitle = {{T}enth {I}nternational {C}onference on {N}umerical {M}ethods in {F}luid {D}ynamics}, editor = {F.G. Zhuang and Y.L. Zhu}, series = {{L}ecture {N}otes in {P}hysics}, year = 1986, publisher = {Springer, Berlin}, pages = {1--7} } @InCollection{feng87tsm, author = {{K}. {F}eng and {M}. {Z}. {Q}in}, title = {The symplectic methods for the computation of {H}amiltonian equations}, booktitle = {{N}umerical {M}ethods for {P}artial {D}ifferential {E}quations}, publisher = {Springer, Berlin}, year = 1987, editor = {Y. L. Zhu and B. Y. Guo}, series = {{L}ecture {N}otes in {M}athematics 1297}, pages = {1--37} } @Book{feng87tsm1, author = {K. Feng}, title = {{T}he {S}ymplectic {M}ethods for {C}omputation of {H}amiltonian {S}ystems}, publisher = {Springer Lecture Notes in Numerical Methods for PDE's}, year = 1987 } @Article{feng89coc, author = {{K}. {F}eng and {M}.{Z}. {Q}in and {D}.{L}. {W}ang}, title = {{C}onstruction of canonical difference schemes for {H}amiltonian formalism via generating functions}, journal = jcm, year = 1989, volume = 7, pages = {71--96} } @Article{feng90sds, author = {{K}.{Q}. Feng and {H}.{M}. Wu and {M}.{Z}. Qin}, title = {{S}ymplectic {D}ifference {S}chemes for {L}inear {H}amiltonian {C}anonical {S}ystems}, journal = jcm, year = 1990, volume = 8, number = 4, pages = {371--380} } @Article{feng91ano, author = {{K}. {F}eng and {D}.{L}. {W}ang}, title = {{A} {N}ote on {C}onservation {L}aws of {S}ymplectic {D}ifference {S}chemes for {H}amiltonian {S}ystems}, journal = jcm, year = 1991, volume = 9, number = 3, pages = {229--237} } @Article{feng91haf1, author = {{K}. {F}eng and {M}.{Z}. Qin}, title = {{H}amiltonian {A}lgorithms for {H}amiltonian {D}ynamical {S}ystems}, journal = pns, year = 1991, volume = 1, number = 2, pages = {105--116} } @Article{feng91haf2, author = {{K}. {F}eng and {M}.{Z}. {Q}in}, title = {{H}amiltonian algorithms for {H}amiltonian systems and a comparative numerical study}, journal = cpc, year = 1991, volume = 65, pages = {173--187} } @Article{feng91sds, author = {{K}. {F}eng and {D}.{L}. Wang}, title = {{S}ymplectic {D}ifference {S}chemes for {H}amiltonian {S}ystems in {G}eneral {S}ymplectic {S}tructure}, journal = jcm, year = 1991, volume = 9, number = 1, pages = {86--96} } @Article{feng91thw, author = {{K}. {F}eng}, title = {{T}he {H}amiltonian {W}ay for {C}omputing {H}amiltonian {D}ynamics}, journal = ma, year = 1991, volume = 56, pages = {17--35} } @Article{feng95vpa, author = {{K}. {F}eng and {Z}.-{J}. {S}hang}, title = {{V}olume-preserving algorithms for source-free dynamical systems}, journal = nm, year = 1995, volume = 71, pages = {451--463} } @InProceedings{forest89cia, author = {{E}. {F}orest and {M}. {B}erz}, title = {{C}anonical {I}ntegration and {A}nalysis of {P}eriodic {M}aps using {N}onstandard {A}nalysis and {L}ie {M}ethods}, booktitle = {Lie Methods in Optics, {II}}, series = {Lecture Notes in Physics}, year = 1989, publisher = {Springer, Berlin}, pages = {47--66} } @Article{forest90fos, author = {{E}. {F}orest and {R}.{D}. {R}uth}, title = {{F}ourth order symplectic integration}, journal = pd, year = 1990, volume = 43, pages = {105--117} } @Article{forest91aot, author = {{E}. Forest and {J}. {B}engtsson and {M}.{F}. {R}eusch}, title = {{A}pplication of the {Y}oshida-{R}uth {T}echniques to {I}mplicit {I}ntegration and {M}ulti-{M}ap {E}xplicit {I}ntegration}, journal = pla, year = 1991, volume = 158, pages = {99--101} } @Article{forest92sol, author = {{E}. {F}orest}, title = {Sixth-order {L}ie group integrators}, journal = jcp, year = 1992, volume = 99, pages = {209--213} } @Article{forester94omt, author = {T. Forester and W. Smith}, title = {{O}n {M}ultiple {T}ime-{S}tep {A}lgorithms and the {E}wald {S}um}, journal = molsim, year = 1994, volume = 13, number = 3, pages = {195--204} } @Article{frank97gif, author = {J. Frank and W. Huang and B. 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Skeel}, title = {{T}he {M}ollified {I}mpulse {M}ethod for {O}scillatory {D}ifferential {E}quations}, institution = {Universidad de Valladolid}, year = 1997, number = {1997/5}, address = {Valladolid, Spain} } @Article{ge88lpi, author = {{Z}. {G}e and {J}. {M}arsden}, title = {{L}ie-{P}oisson integrators and {L}ie-{P}oisson {H}amiltonian-{J}acobi theory}, journal = pla, year = 1988, volume = 133, pages = {134--139} } @Article{ge88ota, author = {{Z}. Ge and {K}. Feng}, title = {{O}n the {A}pproximation of {L}inear {H}amiltonian {S}ystems}, journal = jcm, year = 1988, volume = 6, number = 1, pages = {88--97} } @Article{ge91esd, author = {Z. 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Lubich and {M}. {R}oche}, title = {{T}he {N}umerical {S}olution of {D}ifferential-{A}lgebraic {S}ystems by {R}unge-{K}utta {M}ethods}, publisher = {{S}pringer, Berllin}, year = 1989 } @Article{hairer90eor, author = {{E}. {H}airer and {A}. {I}serles and {J}.{M}. {S}anz-{S}erna}, title = {{E}quilibria of {R}unge-{K}utta methods}, journal = nm, year = 1990, volume = 58, pages = {243--254} } @Book{hairer91sod, author = {{E}. {H}airer and {G}. {W}anner}, title = {{S}olving {O}rdinary {D}ifferential {E}quations {II}, {S}tiff and {D}ifferential-{A}lgebraic {P}roblems}, publisher = {{S}pringer, {B}erlin}, year = 1991 } @InProceedings{hairer93bao, author = {{E}. {H}airer}, title = {{B}ackward analysis of numerical integrators and symplectic methods}, booktitle = {{S}cientific {C}omputation and {D}ifferential {E}quations}, editor = {{K}. {B}urrage and {C}. {B}aker and {P}. v.d.\ {H}ouwen and {Z}. {J}ackiewicz and {P}. {S}harp}, volume = 1, series = annalsnm, year = 1994, publisher = {J.C.\ Baltzer}, address = {Amsterdam}, pages = {107--132}, note = {Proceedings of the SCADE'93 conference, Auckland, New-Zealand, January 1993} } @Unpublished{hairer93tne, author = {{E}. {H}airer and {A}. {M}urua and {J}.{M}. {S}anz-{S}erna}, title = {{T}he non-existence of symplectic multi-derivative {R}unge-{K}utta methods}, note = {{P}reprint}, year = 1993 } @TechReport{hairer95rlt, author = {{E}. {H}airer and {D}. {S}toffer}, title = {{R}eversible long-term integration with variable step sizes}, institution = {{D}ept.\ of {M}ath., {U}niv.\ of {G}eneva, {S}witzerland}, year = 1995 } @Unpublished{hairer97ito, author = {E. Hairer and C. Lubich}, title = {{I}nvariant tori of dissipatively perturbed {H}amiltonian systems under symplectic discretization}, note = {To appear}, year = 1997 } @TechReport{hairer97obf, author = {E. Hairer and P. Leone}, title = {{O}rder barriers for symplectic multi-value methods}, institution = {{U}niversit{\'e} de G{\`e}neve, D{\'e}pt. de math{\'e}matiques}, year = 1997 } @TechReport{hairer97vts, author = {E. Hairer}, title = {{V}ariable time step integration with symplectic methods}, institution = {Universit{\'e} de G{\`e}neve, D{\'e}pt.\ de math{\'e}matiques}, year = 1997, note = {To appear in "Applied Numerical Mathematics"} } @Article{hankel97amd, author = {M. Hankel and B. Karas{\"o}zen and P. Rentrop and U. Schmitt}, title = {{A} {M}olecular {D}ynamics {M}odel for {S}ymplectic {I}ntegrators}, journal = mmos, year = 1997, volume = 3, number = 4, pages = {282--296} } @Unpublished{hardy97svs, author = {D. J. Hardy and D. I. Okunbor and R. D. Skeel}, title = {{S}ymplectic {V}ariable {S}tepsize {I}ntegration for $N$-{B}ody {P}roblems}, note = {To appear}, year = 1997 } @Article{henon64tao, author = {{M}. {H}{\'{e}}non and {C}. {H}eiles}, title = {{T}he applicability of the third integral of motion: some numerical experiments}, journal = aj, year = 1964, volume = 69, pages = {73--79} } @Article{herbst92nhi, author = {{B}.{M}. {H}erbst and {M}.{J}. {A}blowitz}, title = {{N}umerical homoclinic instabilities in the sine-{G}ordon equation}, journal = qm, year = 1992, volume = 15, pages = {345--363} } @Article{herbst93ncs, author = {{B}.{M}. {H}erbst and {M}.{J}. {A}blowitz}, title = {{N}umerical chaos, symplectic integrators and exponentially small splitting distances}, journal = jcp, year = 1993, volume = 105, pages = {122--132} } @Article{herbst94smf, author = {B. M. Herbst and F. Varadi and M. J. Ablowitz}, title = {Symplectic methods for the nonlinear Schr{\"{o}}dinger equation}, journal = mcis, year = 1994, volume = 37, pages = {353--369} } @Unpublished{hochbruck97abo, author = {M. Hochbruck and C. Lubich}, title = {{A} bunch of time integrators for quantum/classical molecular dynamics}, note = {Submitted to {A}lgorithms for {M}acromolecular {M}odelling (P. Deuflhard, J. Hermans, B. Leimkuhler, A. Mark, S. Reich and R. D. Skeel, eds.), Springer Lecture Notes in Computational Science and Engineering}, year = 1997 } @Article{hofbauer96edf, author = {J. Hofbauer}, title = {{E}volutionary dynamics for bimatrix games: {A} {H}amiltonian system?}, journal = {J. Math. Biol}, year = 1996, volume = 34, pages = {675--688} } @Article{huang91aha, author = {{M}. {H}uang}, title = {{A} {H}amiltonian approximation to simulate solitary waves of the {K}orteweg-de {V}ries equation}, journal = mc, year = 1991, volume = 56, pages = {607--620} } @Article{huang97tav, author = {W. Huang and B. Leimkuhler}, title = {{T}he adaptive {V}erlet method}, journal = sisc, year = 1997, volume = 18, number = 1, pages = {239} } @Article{humphreys94amt, author = {D. D. Humphreys and R. A. Friesner and B. J. Berne}, title = {{A} {M}ultiple-{T}ime-{S}tep {M}olecular {D}ynamics {A}lgorithm for {M}acromolecules}, journal = jpc, year = 1994, volume = 98, number = 27, pages = {6685--6892} } @TechReport{humpries92rkm, author = {A. R. Humpries and A. M. Stuart}, title = {{R}unge-{K}utta {M}ethods for {D}issipative and {G}radient {D}ynamical {S}ystems}, institution = {Numerical Analysis Project, Computer Science Department, Stanford University}, year = 1992, number = {{NA}-92-17} } @Article{iserles90sad, author = {{A}. {I}serles}, title = {{S}tability and dynamics of numerical methods for ordinary differential equations}, journal = imajna, year = 1990, volume = 10, pages = {1--30} } @Article{iserles91aua, author = {{A}. {I}serles and {A}.{T}. {P}eplow and {A}.{M}. {S}tuart}, title = {{A} unified approach to spurious solutions introduced by time discretization. {P}art {I}: {B}asic theory}, journal = sijna, year = 1991, volume = 28, pages = {1723--1751} } @Article{iserles91erk, author = {{A}. {I}serles}, title = {{E}fficient {R}unge-{K}utta methods for {H}amiltonian equations}, journal = bhms, year = 1991, volume = 32, pages = {3--20} } @Book{iserles91os, author = {{A}. {I}serles and {S}.{P}. {N}{\o}rsett}, title = {{O}rder {S}tars}, publisher = {{C}hapman {\&} {H}all}, year = 1991 } @Article{iserles92aua, author = {{A}. {I}serles and {A}.{M}. {S}tuart}, title = {{A} unified approach to spurious solutions introduced by time discretization. {P}art {II}: {BDF}-like methods}, journal = imajna, year = 1992, volume = 12, pages = {487--501} } @TechReport{iserles97inj, author = {A. 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Merzel}, title = {{A}n {E}fficient {S}ymplectic {I}ntegration {A}lgorithm for {M}olecular {D}ynamics {S}imulations}, journal = jcics, year = 1995, volume = 35, pages = {321--326} } @Article{janezic95snm, author = {D. Janezic}, title = {{S}ymplectic {N}umerical {M}ethods for {M}olecular {D}ynamics {S}imulation}, journal = bioj, year = 1995, volume = 68, pages = {{A}341} } @InProceedings{janezic96mds, author = {D. Janezic and F. Merzel}, title = {{M}olecular {D}ynamics {S}imulations of {M}acromolecules: {I}mprovements on {C}omputational {E}fficiency}, booktitle = {{P}roceedings of the {I}nternational {W}orkshop {PARALLEL} {NUMERICS} '96}, editor = {R. Trobec and M. Vajtersic and P. Zinterhof and J. Silc and B. Robic}, year = 1996, organization = {{I}nstitut {J}ozef {S}tefan}, address = {{L}jubljana, {S}lovenia}, pages = {17--27}, note = {({ISBN} 86-80023-25-6)} } @Article{janezic96som, author = {D. Janezic and F. Merzel}, title = {{S}imulations of {M}acromolecules: {I}mprovements of {MD} {E}fficiency}, journal = pibmb, year = 1996, volume = {65, {S}1}, pages = {{P}-{A}3-34, 48} } @PhdThesis{jay94rkt, author = {L. O. Jay}, title = {{R}unge-{K}utta type methods for index three differential-algebraic equations with applications to {H}amiltonian systems}, school = {{D}epartment of {M}athematics, {U}niversity of {G}eneva, {S}witzerland}, year = 1994 } @Unpublished{jay96spf, author = {L. O. Jay}, title = {{S}tructure-preservation for constrained dynamics with super partitioned additive {R}unge-{K}utta methods}, note = {to appear in {SIAM} {J}. {S}ci. {C}omput.}, year = 1996 } @Article{jay96spr, author = {{L}. {O}. {J}ay}, title = {{S}ymplectic partitioned {R}unge-{K}utta methods for constrained {H}amiltonian systems}, journal = sijna, year = 1996, volume = 33, pages = {368--387} } @TechReport{jay97liw, author = {L. O. 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Shang}, title = {{V}olume-{P}reserving {A}lgorithms for {S}ource-{F}ree {D}ynamical {S}ystems}, journal = nm, year = 1995, volume = 75, number = 4, pages = {451--463} } @Article{karasozen96cif, author = {B. Karas{\"o}zen}, title = {{C}omposite {I}ntegrators for {B}i-{H}amiltonian {S}ystems}, journal = cmwa, year = 1996, volume = 32, pages = {79--86} } @InProceedings{karasozen96cor, author = {B. Karas{\"o}zen}, title = {{C}omparison of {R}eversible {I}ntegrators for a {H}amiltonian in {N}ormal {F}orm}, booktitle = {{P}roceedings of the {T}hird {I}nternational {C}ongress on {I}ndustrial and {A}pplied {M}athematics, {ICIAM} 95, {I}ssue 4: {A}pplied {S}ciences, especially {M}echanics ({M}inisymposia)}, editor = {{E}. {K}reuzer and {O}. {M}ahrenholz}, year = 1996, pages = {563--566} } @TechReport{karasozen96nso, author = {B. Karas{\"o}zen}, title = {{N}umerical {S}tudies on a {B}i-{H}amiltonian {H}{\'e}non-{H}eiles {S}ystem}, institution = {{M}iddle {E}ast {T}echnical {U}niversity, {D}epartment of {M}athematics}, year = 1996, number = {{N}o 133}, address = {{A}nkara, {T}urkey} } @Unpublished{karasozen96rkm, author = {B. Karas{\"o}zen}, title = {{R}unge-{K}utta methods for {H}amiltonian systems in non-standard symplectic two-form}, note = {Submitted}, year = 1996 } @TechReport{karasozen97rmf, author = {B. Karas{\"o}zen}, title = {Reflexive methods for dynamical systems with conserved quantities}, institution = {Technische Hochschule Darmstadt, FB Mathematik}, year = 1997, number = {Nr.\ 1897} } @Article{kirchgraber88aos, author = {{U}. {K}irchgraber}, title = {{A}n {ODE}-solver based on the method of averaging}, journal = nm, year = 1988, volume = 53, pages = {621--652} } @TechReport{kol97asm, author = {A. Kol and B. Laird and B. Leimkuhler}, title = {{A} symplectic method for rigid-body molecular simulation}, institution = {Department of Applied Mathematics and Theoretical Physics, University of Cambridge}, year = 1997, number = {1997/{NA}5} } @InProceedings{koseleff93raf, author = {P. V. Koseleff}, title = {{R}elations {A}mong {F}ormal {L}ie {S}eries and {C}onstruction of {S}ymplectic {I}ntegrators}, booktitle = {{A}pplied {A}lgebra, {A}lgebraic {A}lgorithms and {E}rror-{C}orrecting {C}odes}, editor = {{G}. {C}ohen and {T}. {M}ora and {O}. {M}oreno}, year = 1993, publisher = {{S}pringer-{V}erlag}, pages = {212--230} } @InCollection{koseleff96esf, author = {P. V. Koseleff}, title = {{E}xhaustive {S}earch for {S}ymplectic {I}ntegators {U}sing {C}omputer {A}lgebra}, booktitle = {{I}ntegration {A}lgorithms and {C}lassical {M}echanics}, publisher = {American Mathematical Society}, year = 1996, editor = {J. E. Mardsen and G. W. Patrick and W. F. Shadwick}, pages = {103--120} } @Book{kozlov95sta, author = {V. V. Kozlov}, title = {{S}ymmetries, {T}oplogy, and {R}esonances in {H}amiltonian {M}echanics}, publisher = {Springer-Verlag}, year = 1995 } @Book{lambert91nmf, author = {{J}.{D}. {L}ambert}, title = {{N}umerical {M}ethods for {O}rdinary {D}ifferential {E}quations, {T}he {I}nitial {V}alue {P}roblem}, publisher = {{W}iley, {C}hichester}, year = 1991 } @Article{lasagni88crk, author = {{F}.{M}. {L}asagni}, title = {{C}anonical {R}unge-{K}utta methods}, journal = zamp, year = 1988, volume = 39, pages = {952--953} } @Unpublished{lasagni90imf, author = {{F}.{M}. {L}asagni}, title = {{I}ntegration methods for {H}amiltonian differential equations}, note = {Unpublished manuscript}, year = 1990 } @TechReport{leimkuhler94daw, author = {B. Leimkuhler}, title = {{D}iscretization and {W}eak {I}nvariants}, institution = {Department of Mathematics, University of Kansas}, year = 1994 } @TechReport{leimkuhler94imf, author = {B. J. Leimkuhler and S. Reich and R. D. Skeel}, title = {{I}ntegration methods for molecular dynamics}, institution = {Kansas Institute for Theoretical and Computational Science, University of Kansas}, year = 1994 } @Article{leimkuhler94sio, author = {{B}. Leimkuhler and {S}. {R}eich}, title = {{S}ymplectic {I}ntegration of {C}onstrained {H}amiltonian {S}ystems}, journal = mc, year = 1994, volume = 63, number = 208, pages = {589--606} } @Article{leimkuhler94sni, author = {{B}. Leimkuhler and {R}.{D}. {S}keel}, title = {{S}ymplectic numerical integrators in constrained {H}amiltonian systems}, journal = jcp, year = 1994, volume = 112, pages = {117--125} } @InCollection{leimkuhler96imf, author = {B. J. Leimkuhler and S. Reich and R. D. Skeel}, title = {{I}ntegration methods for molecular dynamics}, booktitle = {{M}athematical {A}pproaches to {B}iomolecular {S}tructure and {D}ynamics}, publisher = {{S}pringer-{V}erlag}, year = 1996, editor = {Jill P. Mesirov and Klaus Schulten and De Witt Sumners}, volume = 82, series = {{IMA} {V}olumes in {M}athematics and its {A}pplications} } @Article{leimkuhler97oio, author = {B. J. Leimkuhler and E. S. van Vleck}, title = {{O}rthosymplectic {I}ntegration of {L}inear {H}amiltonian {S}ystems}, journal = nm, year = 1997, volume = 77, number = 2, pages = {269--282} } @TechReport{leimkuhler97rar, author = {B. Leimkuhler}, title = {{R}eversible apaptive reularization {I}: perturbed {K}epler motion and classical atomic trajectories}, institution = {Department of Applied Mathematics and Theoretical Physics, University of Cambridge}, year = 1997, number = {1997/{NA}8} } @Unpublished{leimkuhler??sni, author = {B. J. Leimkuhler and R. D. Skeel}, title = {{S}ymplectic {N}umerical {I}ntegrators in {C}onstrained {H}amiltonian {S}ystems}, note = {To appear} } @InCollection{lewis96caf, author = {D. Lewis and J. C. Simo}, title = {{C}onserving {A}lgorithms for the $N$ {D}imensional {R}igid {B}ody}, booktitle = {{I}ntegration {A}lgorithms and {C}lassical {M}echanics}, publisher = {American Mathematical Society}, year = 1996, editor = {J. E. Mardsen and G. W. Patrick and W. F. Shadwick}, pages = {121--140} } @Article{lewis96tpt, author = {H. R. Lewis and J. W. Bates and J. M. Finn}, title = {{T}ime-{D}ependent {P}erturbation {T}heory for {C}onstruction of {I}nvariants of {H}amiltonian {S}ystems}, journal = pla, year = 1996, volume = 215, pages = {160--166} } @Article{li88asd, author = {{C}.{W}. {L}i and {M}.{Z}. {Q}in}, title = {{A} symplectic difference scheme for the infinite dimensional {H}amiltonian system}, journal = jcam, year = 1988, volume = 6, pages = {164--174} } @Article{liao97sif, author = {X. Liao}, title = {Symplectic integrator for general near-integrable {H}amiltonian systems}, journal = cmda, year = 1997, volume = 66, pages = {243--253} } @Article{littell95eao, author = {T. R. Littell and R. D. Skeel and M. Zhang}, title = {{E}rror {A}nalysis of {S}ymplectic {M}ultiple {T}ime {S}tepping}, journal = sijna, year = 1997, volume = 34, number = 5 } @Article{littell96eao, author = {{T}. {R}. {L}ittell and {R}. {D}. {S}keel and {M}. {Z}hang}, title = {{E}rror {A}nalysis of {S}ymplectic {M}ultiple {T}ime {S}tepping}, journal = sijna, year = 1996, note = {To appear} } @TechReport{lopez-marcos95aes, author = {M. A. L{\'o}pez-Marcos and J. M. Sanz-Serna and R. D. Skeel}, title = {{A}n explicit symplectic integrator with maximal stability interval}, institution = {Departemento de Matem{\'a}tica Aplicada y Computati{\'o}n, Universidad de Valladolid, Spain}, year = 1995, number = {1995/7}, note = {To appear in a book to celebrate Prof. A. R. 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Watson}, year = 1996, publisher = {World Scientific Publishing Co.}, pages = {163--176} } @Article{lopez-marcos97esi, author = {{M}. {L}{\'o}pez-Marcos and {J}. {M}. {S}anz-{S}erna and {R}. {D}. {S}keel}, title = {{E}xplicit {S}ymplectic {I}ntegrators {U}sing {H}essian--{V}ector {P}roducts}, journal = sisc, year = 1997, volume = 18, pages = {223--238} } @Article{lu97asa, author = {X. Lu and R. Schmid}, title = {{A} {S}ymplectic {A}lgorithm for {W}ave {E}quations}, journal = mac, year = 1997, volume = 43, pages = {29--38} } @Article{lu99sio, author = {X. Lu and R. Schmid}, title = {Symplectic Integration of {S}ine-{G}ordon Type Systems}, journal = mcis, year = 1999, volume = 50, pages = {255--263} } @InProceedings{maciejewski94nio, author = {A. J. Maciejewski and J. M. 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Scovel}, title = {{A} {S}urvey of {O}pen {P}roblems in {S}ymplectic {I}ntegration}, booktitle = {{I}ntegration {A}lgorithms and {C}lassical {M}echanics}, publisher = {American Mathematical Society}, year = 1996, editor = {J. E. Mardsen and G. W. Patrick and W. F. Shadwick}, pages = {151--180} } @InProceedings{mclachlan96mos, author = {R. I. McLachlan}, title = {{M}ore on {S}ymplectic {C}orrectors}, booktitle = {{I}ntegration {A}lgorithms and {C}lassical {M}echanics}, editor = {{J}errold {E}. {M}arsden and {G}eorge {W}. {P}atrick and {W}illiam {F}. {S}hadwick}, volume = 10, series = {{F}ields {I}nstitute {C}ommunications}, year = 1996, organization = {{F}ields {I}nstitute}, publisher = {{A}merican {M}athematical {S}ociety}, month = {July} } @TechReport{mclachlan96nit, author = {R. I. McLachlan and G. R. W. Quispel and G. S. Turner}, title = {{N}umerical {I}ntegrators that {P}reserve {S}ymmetries and {R}eversing {S}ymmetries}, institution = {{S}chool of {M}athematics, {L}a{T}robe {U}niversity}, year = 1996 } @TechReport{mclachlan97hfd, author = {R. I. McLachlan and I. Szunyogh and V. Zeitlin}, title = {{H}amiltonian finite-dimensional models of baroclinic instability}, institution = {Mathematics Department, Massey University}, year = 1997 } @TechReport{mclachlan97osp, author = {R. I. McLachlan and S. K. Gray}, title = {Optimal stability polynomials for splitting methods, with applications to the time-dependent Schr{\"{o}}dinger equation}, institution = {Mathematics Department, Massey University}, year = 1997 } @Article{mclachlan98gff, author = {R. I. McLachlan and G. R. W. Quispel}, title = {{G}enerating functions for dynamical systems with symmetries, integrals, and differential invariants}, journal = pd, year = 1998, volume = 112, pages = {298--309} } @Article{medan96tbh, author = {C. 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Miesbach}, title = {{S}ymplektische {P}hasenflu{\ss}approximation zur {N}umerischen {I}ntegration {K}anonischer {D}ifferentialgleichungen}, school = {Technische Universit{\"a}t M{\"u}nchen}, year = 1989 } @Article{miesbach92spf, author = {{S}. {M}iesbach and {H}.{J}. {P}esch}, title = {{S}ymplectic phase flow approximation for the numerical integration of canonical systems}, journal = nm, year = 1992, volume = 61, pages = {501--521} } @TechReport{mitchell90nso, author = {A. R. Mitchell and B. A. Murray and B. D. Sleeman}, title = {{N}umerical solution of {H}amiltonian systems in reaction-diffusion by symplectic schemes}, institution = {University of Dundee, Department of Mathematics and Computer Science}, year = 1990, number = {{NA}/122} } @TechReport{murua97ocf, author = {A. Murua and J. M. Sanz-Serna and R. D. Skeel}, title = {Order conditions for numerical integrators obtained by composing simpler methods}, institution = {Departemento de Matem{\'{a}}tica Aplicada y Computati{\'{o}}n, Universidad de Valladolid, Spain}, year = 1997, number = {1997/7} } @Article{nakamura94otd, author = {Y. Nakamura and T. Hashimato}, title = {{O}n the discretization of the three-dimensional {V}olterra systems}, journal = pla, year = 1994, volume = 193, pages = {42--46} } @Article{nambu73ghd, author = {Y. Nambu}, title = {{G}eneralized {H}amiltonian dynamics}, journal = prd, year = 1973, volume = 7, pages = {2405--2412} } @Article{neishtadt84tso, author = {{A}.{I}. {N}eishtadt}, title = {{T}he separation of motions in systems with rapidly rotating phase}, journal = jamm, year = 1984, volume = 48, pages = {133--139} } @Article{nettesheim96aea, author = {P. Nettesheim and F. A. Bornemann, B. Schmidt, C. 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Okunbor}, title = {{C}anonical {M}ethods for {H}amiltonian {S}ystems: {N}umerical {E}xperiments}, journal = pd, year = 1992, volume = 60, pages = {314--322} } @Article{okunbor92ecm, author = {{D}. {O}kunbor and {R}.{D}. {S}keel}, title = {{E}xplicit canonical methods for {H}amiltonian systems}, journal = mc, year = 1992, volume = 59, pages = {439--455} } @Article{okunbor93vss, author = {{D}. {O}kunbor}, title = {{V}ariable step size does not harm second-order integrators for {H}amiltonian systems}, journal = jcam, year = 1993, volume = 47, pages = {273--279} } @Article{okunbor94cnm, author = {{D}. {O}kunbor and {R}.{D}. {S}keel}, title = {{C}anonical numerical methods for molecular dynamics simulations}, journal = jcc, year = 1994, volume = 15, pages = {72--79} } @Article{okunbor94crk, author = {{D}. {O}kunbor and {R}.{D}. {S}keel}, title = {{C}anonical {R}unge-{K}utta-{N}ystr{\"{o}}m {M}ethods of {O}rders 5 and 6}, journal = jcam, year = 1994, volume = 51, number = 3, pages = {375--382} } @Article{okunbor95ecl, author = {E. 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