Total variation diminishing Runge-Kutta schemes

Authors:
Sigal Gottlieb and Chi-Wang Shu

Journal:
Math. Comp. **67** (1998), 73-85

MSC (1991):
Primary 65M20, 65L06

DOI:
https://doi.org/10.1090/S0025-5718-98-00913-2

MathSciNet review:
1443118

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Abstract | References | Similar Articles | Additional Information

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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Additional Information

**Sigal Gottlieb**

Affiliation:
Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912

Email:
sg@cfm.brown.edu

**Chi-Wang Shu**

Affiliation:
Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912

Email:
shu@cfm.brown.edu

DOI:
https://doi.org/10.1090/S0025-5718-98-00913-2

Keywords:
Runge-Kutta method,
high order,
TVD,
low storage

Received by editor(s):
June 10, 1996

Additional Notes:
The first author was supported by an ARPA-NDSEG graduate student fellowship.

Research of the second author was supported by ARO grant DAAH04-94-G-0205, NSF grant DMS-9500814, NASA Langley grant NAG-1-1145 and contract NAS1-19480 while the author was in residence at ICASE, NASA Langley Research Center, Hampton, VA 23681-0001, and AFOSR Grant 95-1-0074.

Article copyright:
© Copyright 1998
American Mathematical Society