An Iterative Finite-Difference Method for Hyperbolic Systems
- 1 July 1969
- journal article
- Published by JSTOR in Mathematics of Computation
- Vol. 23 (107) , 549-565
- https://doi.org/10.2307/2004383
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.Keywords
This publication has 4 references indexed in Scilit:
- Difference Methods for Initial-Value ProblemsMathematics of Computation, 1968
- Finite-Difference Methods for Nonlinear Hyperbolic SystemsMathematics of Computation, 1968
- On certain finite difference schemes for hyperbolic systemsMathematics of Computation, 1964
- Systems of conservation lawsCommunications on Pure and Applied Mathematics, 1960