An iterative finite-difference method for hyperbolic systems

Authors:
S. Abarbanel and G. Zwas

Journal:
Math. Comp. **23** (1969), 549-565

MSC:
Primary 65.67

DOI:
https://doi.org/10.1090/S0025-5718-1969-0247783-2

MathSciNet review:
0247783

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Abstract: An iterative finite-difference scheme for initial value problems is presented. It is applied to the quasi-linear hyperbolic system representing the one-dimensional time dependent flow of a compressible polytropic gas. The emphasis in this research was on the handling of discontinuities, such as shock waves, and overcoming the post-shock oscillations resulting from nonlinear instabilities. The linear stability is investigated as well. The success of the method is indicated by the *monotonic* profiles which were obtained for almost all the cases tested.

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DOI:
https://doi.org/10.1090/S0025-5718-1969-0247783-2

Article copyright:
© Copyright 1969
American Mathematical Society