Boundary conditions for a fourth order hyperbolic difference scheme
HTML articles powered by AMS MathViewer
- by D. M. Sloan PDF
- Math. Comp. 41 (1983), 1-11 Request permission
Abstract:
Oliger [6] has used a stable time-averaged boundary condition with a fourth order leap-frog scheme for the numerical solution of hyperbolic partial differential equations. Gary [3] generalized the time-averaged boundary condition by including a scalar parameter. This paper examines the stability and accuracy of the more general boundary condition. The limit of the stability interval is found for the parameter, and it is shown that the parameter should be given a value close to this limit in order to minimize the boundary errors. Numerical experiments are described which support the theoretical predictions.References
- Eugene Allgower and Kurt Georg, Simplicial and continuation methods for approximating fixed points and solutions to systems of equations, SIAM Rev. 22 (1980), no. 1, 28–85. MR 554709, DOI 10.1137/1022003 C. B. Garcia & T. Y. Li, On a Path Following Method for Systems of Equations, Report 1983, MRC, University of Wisconsin, Madison, 1979.
- John Gary, On boundary conditions for hyperbolic difference schemes, J. Comput. Phys. 26 (1978), no. 3, 339–351. MR 494997, DOI 10.1016/0021-9991(78)90074-8
- Bertil Gustafsson, Heinz-Otto Kreiss, and Arne Sundström, Stability theory of difference approximations for mixed initial boundary value problems. II, Math. Comp. 26 (1972), 649–686. MR 341888, DOI 10.1090/S0025-5718-1972-0341888-3 T. Y. Li & J. A. Yorke, A Simple Reliable Numerical Algorithm for Following Homotopy Paths, Report 1984, MRC, University of Wisconsin, Madison, 1979.
- Joseph Oliger, Fourth order difference methods for the initial boundary-value problem for hyperbolic equations, Math. Comp. 28 (1974), 15–25. MR 359344, DOI 10.1090/S0025-5718-1974-0359344-7
- D. M. Sloan, Stability and accuracy of a class of numerical boundary conditions for the advection equation, IMA J. Numer. Anal. 1 (1981), no. 3, 285–301. MR 641311, DOI 10.1093/imanum/1.3.285
- Hansjörg Wacker (ed.), Continuation methods, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1978. MR 0483273
Additional Information
- © Copyright 1983 American Mathematical Society
- Journal: Math. Comp. 41 (1983), 1-11
- MSC: Primary 65M10
- DOI: https://doi.org/10.1090/S0025-5718-1983-0701620-5
- MathSciNet review: 701620