On convergence of numerical schemes for

hyperbolic conservation laws with

stiff source terms

Author:
Abdallah Chalabi

Journal:
Math. Comp. **66** (1997), 527-545

MSC (1991):
Primary 35L65, 65M05, 65M10

MathSciNet review:
1397441

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Abstract: We deal in this study with the convergence of a class of numerical schemes for scalar conservation laws including stiff source terms. We suppose that the source term is dissipative but it is not necessarily a Lipschitzian function. The convergence of the approximate solution towards the entropy solution is established for first and second order accurate MUSCL and for splitting semi-implicit methods.

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Additional Information

**Abdallah Chalabi**

Affiliation:
CNRS-UMR MIP 5640 - UFR MIG Universite P. Sabatier, 118, route de Narbonne 31062 Toulouse cedex France

Email:
chalabi@mip.ups-tlse.fr

DOI:
https://doi.org/10.1090/S0025-5718-97-00817-X

Keywords:
Conservation laws,
stiff source term,
Runge-Kutta method,
splitting method,
implicit scheme,
TVD,
TVB scheme,
entropy solution

Received by editor(s):
September 19, 1995

Received by editor(s) in revised form:
March 29, 1996

Article copyright:
© Copyright 1997
American Mathematical Society