Convergence theorem for difference approximations of hyperbolic quasilinear initialboundary value problems
Author:
Daniel Michelson
Journal:
Math. Comp. 49 (1987), 445459
MSC:
Primary 65N10; Secondary 65M10
MathSciNet review:
906181
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Abstract: Dissipative difference approximations to multidimensional hyperbolic quasilinear initialboundary value problems are considered. The difference approximation is assumed to be consistent with the differential problem and its linearization should be stable in . A formal asymptotic expansion to the difference solution is constructed. This expansion includes boundary and initial layers. It is proved that the expansion indeed approximates the difference solution to the required order. As a result, the difference solution converges to the differential one as the mesh size h tends to 0.
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DOI:
http://dx.doi.org/10.1090/S00255718198709061817
PII:
S 00255718(1987)09061817
Article copyright:
© Copyright 1987
American Mathematical Society
