Stability of numerical schemes solving quasilinear wave equations
Author:
A. Y. le Roux
Journal:
Math. Comp. 36 (1981), 93105
MSC:
Primary 65M10; Secondary 35L67
MathSciNet review:
595044
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Abstract: A generalization of the Riemann invariants for quasilinear wave equations of the type , which includes the shock curves, is proposed and is used to solve the Riemann problem. Three numerical schemes, whose accuracy is of order one (the LaxFriedrichs scheme and two extensions of the upstreaming scheme), are constructed by projection, onto piecewise constant functions, of the solutions of a set of Riemann problems. They are stable in the norm for a class of wave equations, including a nonlinear model of extensible strings, which are not genuinely nonlinear. The problem with boundary conditions is detailed, as is its treatment, by the numerical schemes.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0025571819810595044X
PII:
S 00255718(1981)0595044X
Article copyright:
© Copyright 1981
American Mathematical Society
