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Mathematics of Computation

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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
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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Article copyright: © Copyright 1969 American Mathematical Society