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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


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


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.
    M. Carpenter and J. Otto, High-order cyclo-difference techniques: A new methodology for finite differences, Tech. report, ICASE, NASA Langley Research Center, Hampton, VA 23681-0001, 1993.
  • Mark H. Carpenter, David Gottlieb, and Saul Abarbanel, Time-stable boundary conditions for finite-difference schemes solving hyperbolic systems: methodology and application to high-order compact schemes, J. Comput. Phys. 111 (1994), no. 2, 220–236. MR 1275021, DOI 10.1006/jcph.1994.1057
  • Heinz-Otto Kreiss and Jens Lorenz, Initial-boundary value problems and the Navier-Stokes equations, Pure and Applied Mathematics, vol. 136, Academic Press, Inc., Boston, MA, 1989. MR 998379
  • Carl de Boor (ed.), Mathematical aspects of finite elements in partial differential equations, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1974. Publication No. 33 of the Mathematics Research Center, The University of Wisconsin-Madison. MR 0349031
  • —, On the existence of energy estimates for difference approximations for hyperbolic systems, Tech. Report, Dept. of Scientific Computing, Uppsala University, 1977. P. Olsson, Stable approximation of symmetric hyperbolic and parabolic equations in several space dimensions, Tech. Report 138, Dept. of Scientific Computing, Uppsala Univ., Uppsala, Sweden, December 1991.
  • Pelle Olsson, Summation by parts, projections, and stability. II, Math. Comp. 64 (1995), no. 212, 1473–1493. MR 1308459, DOI 10.1090/S0025-5718-1995-1308459-9
  • G. Scherer, Numerical computations with energy estimates schemes, Tech. report, Dept. of Scientific Computing, Uppsala Univ., Uppsala, Sweden, April 1977. In PhD thesis by G. Scherer, 1977.
  • Bo Strand, Summation by parts for finite difference approximations for $d/dx$, J. Comput. Phys. 110 (1994), no. 1, 47–67. MR 1259900, DOI 10.1006/jcph.1994.1005
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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Math. Comp. 64 (1995), 1035-1065
  • MSC: Primary 65M06; Secondary 65M12
  • DOI:
  • MathSciNet review: 1297474