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Mathematics of Computation

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Convergence of relaxation schemes
for hyperbolic conservation laws
with stiff source terms

Author: A. Chalabi
Journal: Math. Comp. 68 (1999), 955-970
MSC (1991): Primary 35L65, 65M05, 65M10
Published electronically: February 10, 1999
MathSciNet review: 1648367
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Abstract: We focus in this study on the convergence of a class of relaxation numerical schemes for hyperbolic scalar conservation laws including stiff source terms. Following Jin and Xin, we use as approximation of the scalar conservation law, a semi-linear hyperbolic system with a second stiff source term. This allows us to avoid the use of a Riemann solver in the construction of the numerical schemes. The convergence of the approximate solution toward a weak solution is established in the cases of first and second order accurate MUSCL relaxed methods.

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Additional Information

A. Chalabi
Affiliation: CNRS, Umr Mip 5640 - UFR Mig Universite P. Sabatier, Route de Narbonne 31062 Toulouse cedex France

Keywords: Conservation laws, stiff source term, relaxation scheme, fully implicit scheme, semi-implicit scheme, TVD scheme, MUSCL method, entropy solution
Received by editor(s): April 29, 1997
Received by editor(s) in revised form: October 14, 1997
Published electronically: February 10, 1999
Article copyright: © Copyright 1999 American Mathematical Society