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Total variation diminishing Runge-Kutta schemes
- Source :
- Mathematics of Computation. 67:73-85
- Publication Year :
- 1998
- Publisher :
- American Mathematical Society (AMS), 1998.
-
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.
Details
- ISSN :
- 10886842 and 00255718
- Volume :
- 67
- Database :
- OpenAIRE
- Journal :
- Mathematics of Computation
- Accession number :
- edsair.doi...........42203241455cdc962205fda327055283