Total Variation Diminishing Runge-Kutta Schemes.
INSTITUTE FOR COMPUTER APPLICATIONS IN SCIENCE AND ENGINEERING HAMPTON VA
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In this paper we further explore a class of high order TVD total variation diminishing Runge-Kutta time discretization initialized in Shu Osher 1988, 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.
- Numerical Mathematics