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Convergence Theorem for Difference Approximations of Hyperbolic Quasi- Initial-Boundary Value Problems

Daniel Michelson
Mathematics of Computation
Vol. 49, No. 180 (Oct., 1987), pp. 445-459
DOI: 10.2307/2008321
Stable URL: http://www.jstor.org/stable/2008321
Page Count: 15
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Convergence Theorem for Difference Approximations of Hyperbolic Quasi- Initial-Boundary Value Problems
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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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