Total variation diminishing Runge-Kutta schemes

Gottlieb, Sigal; Shu, Chi-Wang

doi:10.1090/S0025-5718-98-00913-2

Total variation diminishing Runge-Kutta schemes
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by Sigal Gottlieb and Chi-Wang Shu PDF

Math. Comp. 67 (1998), 73-85 Request permission

Abstract:

In this paper we further explore a class of high order TVD (total variation diminishing) Runge-Kutta time discretization initialized in a paper by Shu and Osher, suitable for solving hyperbolic conservation laws with stable spatial discretizations. We illustrate with numerical examples that non-TVD but linearly stable Runge-Kutta time discretization can generate oscillations even for TVD (total variation diminishing) spatial discretization, verifying the claim that TVD Runge-Kutta methods are important for such applications. We then explore the issue of optimal TVD Runge-Kutta methods for second, third and fourth order, and for low storage Runge-Kutta methods.

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