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Mathematics of Computation

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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

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