High Order Asymptotically Strong-Stability-Preserving Methods for Hyperbolic Systems with Stiff Relaxation

In this not e we report some recent result on the time discretization of hyperbolic systems of conservation laws with stiff relaxation terms. The formalism of Implicit-Explicit (IMEX) Runge-Kutta methods is essential in the derivation and analysis of the schemes. Here we restrict to diagonally implicit schemes and consider the development of schemes up to order 3 that are asymptotic-preserving (AP) and strong-stability-preserving (SSP) for the limiting system of conservation laws.

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