Preprint 2001-037

Higher-Order Relaxation Schemes for Hyperbolic Systems of Conservation Laws

Mapundi Banda and Mohammed Seaid

Abstract: We present a higher order generalisation for relaxation methods in the framework presented by Jin and Xin. The schemes employ general higher order integration for spatial discretisation and higher order implicit-explicit schemes or Total Variation diminishing (TVD) Runge-Kutta schemes for time integration of relaxed or relaxing schemes, respectively, for time integration. Numerical experiments are performed on various test problems, in particular, the Euler equations of inviscid gas dynamics. In addition, uniform convergence with respect to the relaxation parameter is demonstrated.

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Mapundi Banda, <>
Mohammed Seaid, <>
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