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Mathematics of Computation

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Existence and uniqueness of traveling waves and error estimates for Godunov schemes of conservation laws

Author: Haitao Fan
Journal: Math. Comp. 67 (1998), 87-109
MSC (1991): Primary 65M10, 35L65
MathSciNet review: 1451320
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Abstract: The existence and uniqueness of the Lipschitz continuous traveling wave of Godunov’s scheme for scalar conservation laws are proved. The structure of the traveling waves is studied. The approximation error of Godunov’s scheme on single shock solutions is shown to be $O(1)\Delta x$.

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Additional Information

Haitao Fan
Affiliation: Department of Mathematics, Georgetown University, Washington, DC 20057

Received by editor(s): February 9, 1996
Received by editor(s) in revised form: August 19, 1996
Additional Notes: Research supported by NSF Fellowship under Grant DMS-9306064.
Article copyright: © Copyright 1998 American Mathematical Society