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We present a higher order generalization for relaxation methods in the framework presented by Jin and Xin in [10]. 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.
Key Words: relaxation methods,; hyperbolic systems,; higher order upwind schemes,; Runge–Kutta methods
Published Online: 2005-09-01
Published in Print: 2005-09-01
Copyright 2005, Walter de Gruyter