%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % % Bibliography-database for the SYNODE Project % % % % Topic: Geometric Integration % % % % Version: % % '$Id: geom_int.bib,v 2.40 2003/03/06 11:00:58 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{ aam = "Acta Applicandae Mathematicae" } @string{ acm = "Adv. Comput. Math." } @string{ an = "Acta Numerica" } @string{ apa = "Acta Phys. Austriaca" } @string{ am = "Advances in Mathematics" } @string{ annalsnm = "Annals of Numer. Math." } @string{ anm = "Appl. Numer. Math." } @string{ arma = "Arch. Rat. Mech. Anal" } @string{ aj = "Astron. J." } @string{ bit = "BIT" } @string{ bhms = "Bull. Hellenic Math. Soc." } @string{ cm = "Celest. Mech." } @string{ cmda = "Celest. Mech. and Dyn. Astro." } @string{ cpam = "Comm. Pure and Appl. Math." } @string{ comp = "Computing" } @string{ cma = "Computers Math. Applic." } @string{ cmame = "Comput. Methods Appl. Mech. Engrg." } @string{ cmda = "Celestial Mechanics and Dynamical Astronomy" } @string{ cmp = "Comm. Math. Phys." } @string{ cpc = "Comput. Phys. Comm." } @string{ dm = "Discrete Methematics" } @string{ etna = "Electronic Transactions on Numerical Analysis" } @string{ fic = "Fields Inst. Com." } @string{ focm = "Foundations of Computational Mathematics" } @string{ hermis = "Hermis" } @string{ ieeetac = "IEEE Trans. Automatic Control" } @string{ ieeetns = "IEEE Trans. Nucl. Sci." } @string{ ijom = "Illinois J. Math." } @string{ imajna = "IMA J. Numer. Anal." } @string{ ijcm = "Internat. J. Comput. Math." } @string{ ijnme = "Internat. J. Numer. Methods Engrg." } @string{ ijss = "Internat. J. Solids Structures" } @string{ jalg = "J. Algebra" } @string{ jamm = "J. Appl. Math. Mech." } @string{ jcam = "J. Comput. Appl. Math" } @string{ jcc = "J. Comput. Chem." } @string{ jcm = "J. Comput. Math." } @string{ jde = "J. Differential Equations" } @string{ jdcs = "J. Dynamical and Control Systems" } @string{ jmaaa = "J. of Math. Anal. and Applic." } @string{ jmsec = "J. of Math. Systems, Estimation, and Control" } @string{ jmsm = "J. Mech. Struct. and Mach." } @string{ jnp = "J. Nath. Phys." } @string{ jnmca = "J. Num. Method and Comp. Appl." } @string{ jcp = "J. of Comp. Phys." } @string{ joc = "J. of Complexity" } @string{ jmaa = "J. of Math. Anal. and Appl." } @string{ jmp = "J. of Math. Phys." } @string{ jns = "J. Nonlinear Sci." } @string{ jpa = "J. Phys. A" } @string{ jpamg = "J. Phys. A: Math. Gen." } @string{ jsc = "Journal of Symbolic Computation" } @string{ leip = "Leipziger Ber." } @string{ lmp = "Letters in Mathematical Physics" } @string{ laa = "Lin. Alg. Applic." } @string{ ma = "Math. Appl." } @string{ mc = "Math. Comp." } @string{ mcis = "Mathematics and Computers in Simulation" } @string{ mic = "Modeling, Identification and Control" } @string{ mwr = "Monthly Weather Rev." } @string{ msd = "Multibody System Dynamics" } @string{ nm = "Numer. Math." } @string{ nonlin = "Nonlinearity" } @string{ npb = "Nuclear Physics B" } @string{ prd = "Physical Review D" } @string{ pd = "Physica D" } @string{ pl = "Phys. Lett." } @string{ pla = "Physics Letters A" } @string{ pr = "Phys. Rep." } @string{ prl = "Physical Review Letters" } @string{ ptrsa = "Phil. Trans. Royal Soc. A" } @string{ prsla = "Proc. R. Soc. Lond. A" } @string{ potlms = "Proc. London Math. Soc." } @string{ pns = "Progr. Natur. Sci." } @string{ qm = "Quaestiones Mathematicae" } @string{ scl = "Systems Control Lett." } @string{ sijam = "SIAM J. Appl. Math." } @string{ sijma = "SIAM J. Math. Anal." } @string{ sijmaa = "SIAM J. Matrix Anal. Applic." } @string{ sijna = "SIAM J. Numer. Anal." } @string{ sisc = "SIAM J. Sci. Comput." } @string{ sir = "SIAM Review" } @string{ zamp = "Z. Angew. Math. Phys." } %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% @Article{ablowitz95ica, author = {M. J. Ablowitz and S. Charkravarty}, title = {Integrability, Computation and Applications}, journal = aam, year = 1995, volume = 39, pages = {5--37} } @Article{ablowitz96otn1, author = {M. J. Ablowitz and B. M. Herbst and C. Schobert}, title = {On the Numerical Solution of the {S}ine-{G}ordon Equation, {I}. {I}ntegrable Discretizations and Homoclinic Manifolds}, journal = jcp, year = 1996, volume = 126, pages = {299--314} } @InCollection{ablowitz96otn2, author = {M. Ablowitz and B. M. Herbst and C. Schober}, title = {On the Numerics of Integrable Discretizations}, booktitle = {CRM Proceedings and Lecture Notes, Volume 6}, publisher = {AMS}, year = 1996, pages = {1--10} } @Article{ablowitz97otn, author = {M. J. Ablowitz and B. M. Herbst and C. Schobert}, title = {On the Numerical Solution of the {S}ine-{G}ordon Equation, {II}. {P}erformance of Numerical Schemes}, journal = jcp, year = 1997, volume = 131, pages = {354--367} } @Book{abraham78fom, author = {R. Abraham and J. E. Marsden}, title = {Foundations of Mechanics}, publisher = {Addison-Wesley}, year = 1978, edition = {{S}econd} } @Book{abraham88mta, author = {R. Abraham and J. E. Marsden and T. Ratiu}, title = {Manifolds, Tensor Analysis, and Applications}, publisher = {Springer-Verlag}, year = 1988, series = {{AMS} 75}, edition = {{S}econd} } @Misc{allen01nea, author = {L. Allen and T. J. Bridges}, title = {Numerical Exterior Algebra and the Compound Matrix Method}, year = 2001 } @Book{arnold89mmo, author = {V. I. Arnold}, title = {Mathematical Methods of Classical Mechanics}, publisher = {Springer-Verlag}, year = 1989, edition = {{GTM} 60, {S}econd }} @Book{arnold98tmi, author = {V. I. Arnold and B. A. Khesin}, title = {Topological Methods in Hydrodynamics}, publisher = {Springer-Verlag}, year = 1998, number = 125, series = {Applied Mathematical Sciences} } @TechReport{arponen96otn, author = {T. Arponen and J. Tuomela}, title = {On the Numerical Solution of Involutive Ordinary Differential Systems: Numerical Results}, institution = {Institute of Mathematics, Helsinki University of Technology}, year = 1996, number = {{A}370} } @Book{arrowsmith92dsd, author = {D. K. Arrowsmith and C. M. Place}, title = {Dynamical Systems: Differential Equations, Maps, and Chaotic Behavior}, publisher = {Chapman \& Hall}, year = 1992, address = {New York} } @Article{ascher91pir, author = {U. M. Ascher and L. R. Petzold}, title = {Projected Implicit {R}unge-{K}utta Methods for Differential-Algebraic Equations}, journal = sijna, volume = 28, year = 1991, pages = {1097--1120} } @Article{ascher92pcm, author = {U. M. Ascher and L. R. Petzold}, title = {Projected Collocation Methods for Higher-Order Higher-Index Differential-Algebraic Equations}, journal = jcam, year = 1992, volume = 43, pages = {243--259} } @Article{ascher93soc, author = {U. M. Ascher and L. R. Petzold}, title = {Stability of Computational Methods for Constrained Dynamics Systems}, journal = sisc, year = 1993, volume = 14, pages = {95--120} } @Article{ascher94sod, author = {U. M. Ascher and H. Chin and S. Reich}, title = {Stabilization of {DAE}s and Invariant Manifolds}, journal = nm, year = 1994, volume = 67, number = 2, pages = {131--149} } @InProceedings{austin91sas, author = {M. Austin and P. S. Krishnaprasad and L.-S. Wang}, title = {Symplectic and Almost Poisson Integration of Rigid Body Systems }, booktitle = {Proceedings of the 1991 International Conference on Computational Engineering Science}, editor = {S. Atluvi}, year = 1991, address = {Melbourne, Australia} } @Article{austin93api, author = {M. Austin and P. S. Krishnaprasad and L.-S. Wang}, title = {Almost Poisson Integration of Rigid Body Systems}, journal = jcp, year = 1993, volume = 107, pages = {105--117} } @Article{azara92amp, author = {J. L. R. Azara}, title = {A {MAPLE} Program for the Generation of the {L}ie-series Solution of Systems of Non-Linear Ordinary Differential Equations}, journal = cpc, year = 1992, volume = 67, pages = {537--542} } @Article{baker05aac, author = {H. F. Baker}, title = {Alternants and continuous groups}, journal = potlms, year = {1905}, volume = {3}, pages = {24--47} } @Article{bakirova97spd, author = {M. I. Bakirova and V. A. Dorodnitsyn and R. V. Kozlov}, title = {Symmetry Preserving Discrete Schemes for some Heat Transfer Equations}, journal = jpamg, year = 1997 } @Book{barr90ctf, author = {M. Barr and C. Wells}, title = {Category Theory for Computing Science}, publisher = {Prentice Hall}, year = 1990 } @Article{barth95smf, author = {E. Barth and B. J. Leimkuhler}, title = {Symplectic Methods for Conservative Multibody Systems}, journal = fic, year = 1995, note = {To appear} } @Article{blanes00iho, author = {S. Blanes and F. Casas and J. Ros}, title = {Improved High Order Integrators Based on the {M}agnus Expansion}, journal = bit, year = 2000, volume = 40, number = 3, pages = {434--450} } @Article{blanes02hoo, author = {S. Blanes and F. Casas and J. Ros}, title = {High Order Optimized Geometric Integrators for Linear Differential Equations}, journal = bit, year = 2002, volume = 42, number = 2, pages = {262--284} } @TechReport{blanes99sm, author = {S. Blanes and P. C. Moan}, title = {Splitting Methods for Non-Autonomous Differential Equations}, institution = {Department of Applied Mathematics and Theoretical Physics}, year = 1999, number = {1999/{NA}21}, address = {University of Cambridge, England} } @Article{bloch96oca, author = {A. M. Bloch and P. E. Crouch}, title = {Optimal Control and Geodesic Flows}, journal = scl, year = 1996, volume = 28, number = 2, pages = {65--72} } @Article{bloch97dbe, author = {A. M. Bloch and R. W. Brockett and P. E. Crouch}, title = {Double Bracket Equations and Geodesic Flows on Symmetric Spaces}, journal = cmp, year = 1997, volume = 187, number = 2, pages = {357--373} } @Book{boothby75ait, author = {W. M. Boothby}, title = {An Introduction to Riemannian Geometry}, publisher = {Academic Press}, year = 1975 } @Article{botsaris, author = {C. A. Botsaris}, title = {Constrained Optimization along Geodesics}, journal = jmaaa, year = 1981, volume = 79, pages = {295--306} } @Unpublished{bottasso97ifr, author = {C. L. Bottasso and M. Borri}, title = {Integrating Finite Rotations}, note = {Preprint submitted to Comp. Methods Appl. Mech. Engrg.}, year = 1997 } @Book{bourbaki75lga, author = {N. Bourbaki}, title = {Lie groups and {L}ie algebras}, publisher = {{P}art {I}, {C}hapters 1--3, Addison-Wesley}, year = 1975 } @Article{brenner98ans, author = {P. Brenner and V. Mehrmann and H. Xu}, title = {A Numerically Stable, Structure Preserving Method for Computing the Eigenvalues of Real {H}amiltonian or Symplectic Pencils}, journal = nm, year = 1998, volume = 78, number = 3, pages = {329--358} } @Article{brockett91dst, author = {R. Brockett}, title = {Dynamical Systems that Sort Lists, Diagonalize Matrices, and Solve Linear Programming Problems}, journal = laa, year = 1991, volume = 146, pages = {79--91} } @Article{brockett94tdb, author = {R. Brockett}, title = {The Double Bracket Equation as the Solution of a Variational Problem}, journal = fic, year = 1994, volume = 3, pages = {69--76} } @InProceedings{bryant95ait, author = {R. L. Bryant}, title = {An Introduction to {L}ie Groups and Symplectic Geometry}, booktitle = {{G}eometry and {Q}uantum {F}ield {T}heory}, editor = {D. S. Freed and K. K. Uhlenbeck}, volume = {1, Second Edition}, series = {IAS/Park City Mathematics Series}, year = 1995, publisher = {American Mathematical Society} } @Misc{budd01gia, author = {C. J. Budd and M. D. Piggott}, title = {Geometric Integration and Its Applications}, year = 2001, note = {To appear in Foundations of Computational Mathematics, a volume of the Handbook of Numerical Analysis, ed. Ph. G. Chiarlet and F. Cucker, published by Elsevier Science} } @InCollection{budd99gin, author = {C. J. Budd and A. Iserles}, title = {Geometric Integration: Numerical Solution of Differential Equations on Manifolds}, booktitle = {Geometric Integration: Numerical Solution of Differential Equations on Manifolds}, publisher = {London Mathematical Society}, year = 1999, editor = {C. J. Budd and A. Iserles}, volume = 357, series = {Philosophical Transactions of the Royal Society A}, pages = {945--956} } @Article{budd99ssn, author = {C. J. Budd and G. J. Collins and W. Z. Huang and R. D. Russell}, title = {Self-Similar Numerical Solutions of the Porous-Medium Equation Using Moving Mesh Methods}, journal = ptrsa, year = 1999, volume = 357, pages = {1047--1078} } @Article{buono01rkt, author = {N. del Buono and L. Lopez}, title = {Runge--{K}utta Type Methods Based on Geodesics for Systems of {ODE}s on the {S}tiefel Manifold}, journal = bit, year = 2001, volume = 41, number = 5, pages = {912--923} } @Article{calvo96rkm1, author = {M. P. Calvo and A. Iserles and A. Zanna}, title = {Runge-{K}utta Methods for Orthogonal and Isospectral Flows}, journal = anm, year = 1996, volume = 22, pages = {153--163} } @InCollection{calvo96rkm2, author = {M. P. Calvo and A. Iserles and A. Zanna}, title = {Runge--{K}utta Methods on Manifolds}, booktitle = {A. R. Mitchell's 75th Birthday Volume}, publisher = {World Scientific}, year = 1996, editor = {D. F. Griffiths and G. A. Watson}, address = {Singapore}, pages = {57--70} } @Article{calvo97nso, author = {M. P. Calvo and A. Iserles and A. Zanna}, title = {Numerical Solution of Isospectral Flows}, journal = mc, year = 1997, volume = 66, number = 220, pages = {1461--1486} } @TechReport{calvo97sem, author = {M. P. Calvo and A. Iserles and A. Zanna}, title = {Semi-Explicit Methods for Isospectral Flows}, institution = {Department of Applied Mathematics and Theoretical Physics}, year = 1997, number = {1997/{NA}16}, address = {University of Cambridge, England}, note = {To appear in {\em Adv.\ Comp.\ Math.}} } @Article{calvo98vsi, author = {M. P. Calvo and M. A. L{\'o}pez-Marcos and J. M. Sanz-Serna}, title = {Variable Step Implementation of Geometric Integrators}, journal = anm, year = 1998, volume = 28, number = 1, pages = {1--16} } @Article{calvo99cmf, author = {M. P. Calvo and A. Iserles and A. Zanna}, title = {Conservative Methods for the {T}oda Lattice Equations}, journal = imajna, year = 1999, volume = 19, number = 4, pages = {509--523} } @Article{campbell97oal, author = {J. E. Campbell}, title = {On a Law of Combination of Operators Bearing on the Theory of Continuous Transformation Groups}, journal = potlms, year = 1897, volume = 28, pages = {381--390} } @Article{cano97egi, author = {B. Cano and J. M. Sanz-Serna}, title = {Error Growth in the Numerical Integration of Periodic Orbits, with Application to {H}amiltonian and Reversible Systems}, journal = sijna, year = 1997, volume = 34, number = 4, pages = {1391--1417} } @Article{cano98egi, author = {B. Cano and J. M. Sanz-Serna}, title = {Error Growth in the Numerical Integration of Periodic Orbits by Multistep Methods, with Application to Reversible Systems}, journal = imajna, year = 1998, volume = 18, number = 1, pages = {57--75} } @Book{carter95lol, author = {R. Carter and G. Segal and I. MacDonald}, title = {Lectures on {L}ie Groups and {L}ie Algebras}, publisher = {London Mathematical Society}, year = 1995, volume = 32, series = {Student Texts} } @Article{casas91laa, author = {F. Casas and J. A. Oteo and J. Ros}, title = {Lie Algebraic Approach to {F}er's Expansion for Classical {H}amiltonian Systems}, journal = jpamg, year = 1991, volume = 24, pages = {4037--4046} } @Article{casas96ffa, author = {F. Casas}, title = {Fer's Factorization as a Symplectic Integrator}, journal = nm, year = 1996, volume = 74, number = 3, pages = {283--303} } @Article{casas96sol, author = {F. Casas}, title = {Solution of Linear Partial Differential Equations by {L}ie Algebraic Methods}, journal = jcam, year = 1996, volume = 76, pages = {159--170} } @Article{celledoni00ate, author = {E. Celledoni and A. Iserles}, title = {Approximating the exponential from a {L}ie algebra to a {L}ie group}, journal = mc, year = 2000, note = {Posted on March 15, PII S 0025-5718(00)01223-0 (to appear in print).} } @Article{celledoni01, author = {E. Celledoni and A. Iserles}, title = {Methods for the Approximation of the Matrix Exponential in a {L}ie-Algebraic Setting}, journal = ijna, year = 2001, volume = 21, number = 2, pages = {463--488} } @Article{celledoni01ano, author = {E. Celledoni}, title = {A Note on the numerical Integration of the {KdV} Equation via Isospectral Deformations}, journal = jpamg, year = 2001, volume = 34, number = 11, pages = {2205--2214} } @TechReport{celledoni01oti, author = {E. Celledoni and B. Owren}, title = {On the Implementation of {L}ie Group Methods on the {S}tiefel Manifold}, institution = {The Norwegian University of Science and Technology, Trondheim, Norway}, year = 2001, number = {Numerics No.\ 9/2001} } @Article{celledoni02ctf, author = {E. Celledoni and A. Iserles and S. P. N{\o}rsett and B. Orel}, title = {Complexity Theory for {L}ie-Group Solvers}, journal = joc, year = 2002, volume = 18, number = 1 } @TechReport{celledoni99ctf, author = {E. Celledoni and A. Iserles and S. P. N{\o}rsett and B. Orel}, title = {Complexity Theory for {L}ie-Group Solvers}, institution = {Department of Applied Mathematics and Theoretical Physics}, year = 1999, number = {1999/{NA}20}, address = {University of Cambridge, England} } @TechReport{celledoni99lgm, author = {E. Celledoni and B. Owren}, title = {Lie Group Methods for Rigid Body Dynamics and Time Integration on Manifolds}, institution = {The Norwegian University of Science and Technology, Trondheim, Norway}, year = 1999 } @TechReport{channell86sif, author = {P. Channell}, title = {Symplectic Integration for Particles in Electric and Magnetic Fields}, institution = {Los Alamos National Laboratory}, year = 1986, type = {{A}ccelerator {T}heory {N}ote, {N}o. {AT}-6: {ATN}-86-5} } @Article{chorin78pfa, author = {A. Chorin and T. J. R. Huges and J. E. Marsden and M. McCracken}, title = {Product Formulas and Numerical Algorithms}, journal = cpam, year = 1978, volume = 31, pages = {205--256} } @Article{cooper87sor, author = {G. J. 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E. Crouch and R. Grossman and Y. Yan }, title = {A Third Order Geometrically Stable {R}unge--{K}utta Algorithm on a Manifold}, year = 1992 } @InProceedings{crouch92tec, author = {P. E. Crouch and R. L. Larson}, title = {The Explicit Computation of Integration Algorithms and First Integrals for Ordinary Differential Equations with Polynomial Coefficients Using Trees}, booktitle = {Proceedings of the 1992 International Symposium of Algebraic and Symbolic Computation}, year = 1992, publisher = {ACM} } @Article{crouch93nio, author = {P. E. Crouch and R. Grossman}, title = {Numerical Integration of Ordinary Differential Equations on Manifolds}, journal = jns, year = 1993, volume = 3, pages = {1--33} } @Article{crouch95otn, author = {P. E. Crouch and Y. Yan and R. Grossman}, title = {On the Numerical Integration of the Rolling Ball Equations Using Geometrically Exact Algorithms}, journal = jmsm, year = 1995, volume = 23, pages = {257--272} } @Article{crouch95tdi, author = {P. E. 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