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Higher-order relaxation schemes for hyperbolic systems of conservation laws
∗ School of Mathematical Sciences, University of KwaZulu-Natal, Private Bag X01, Pietermaritzburg 3209, South Africa
† Fachbereich Mathematik, TU Darmstadt, 64289 Darmstadt, Germany
Citation Information: Journal of Numerical Mathematics jnma. Volume 13, Issue 3, Pages 171–196, ISSN (Online) 1569-3953, ISSN (Print) 1570-2820, DOI: 10.1515/156939505774286102, September 2005
We present a higher order generalization for relaxation methods in the framework presented by Jin and Xin in . The schemes employ general higher order integration for spatial discretization and higher order implicit-explicit (IMEX) schemes or Total Variation diminishing (TVD) Runge–Kutta schemes for time integration of relaxing or relaxed schemes, respectively, for time integration. Numerical experiments are performed on various test problems, in particular, the Burger's and Euler equations of inviscid gas dynamics in both one and two space dimensions. In addition, uniform convergence with respect to the relaxation parameter is demonstrated.