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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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Summation by parts, projections, and stability. I
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by Pelle Olsson PDF
Math. Comp. 64 (1995), 1035-1065 Request permission

Abstract:

We have derived stability results for high-order finite difference approximations of mixed hyperbolic-parabolic initial-boundary value problems (IBVP). The results are obtained using summation by parts and a new way of representing general linear boundary conditions as an orthogonal projection. By rearranging the analytic equations slightly, we can prove strict stability for hyperbolic-parabolic IBVP. Furthermore, we generalize our technique so as to yield stability on nonsmooth domains in two space dimensions. Using the same procedure, one can prove stability in higher dimensions as well.
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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Math. Comp. 64 (1995), 1035-1065
  • MSC: Primary 65M06; Secondary 65M12
  • DOI: https://doi.org/10.1090/S0025-5718-1995-1297474-X
  • MathSciNet review: 1297474