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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Convergence theorem for difference approximations of hyperbolic quasilinear initial-boundary value problems
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by Daniel Michelson PDF
Math. Comp. 49 (1987), 445-459 Request permission

Abstract:

Dissipative difference approximations to multi-dimensional hyperbolic quasi-linear initial-boundary value problems are considered. The difference approximation is assumed to be consistent with the differential problem and its linearization should be stable in ${l_2}$. 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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Additional Information
  • © Copyright 1987 American Mathematical Society
  • Journal: Math. Comp. 49 (1987), 445-459
  • MSC: Primary 65N10; Secondary 65M10
  • DOI: https://doi.org/10.1090/S0025-5718-1987-0906181-7
  • MathSciNet review: 906181