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Continuous and numerical analysis of a boundary shock problem

Published online by Cambridge University Press:  17 April 2009

Relja Vulanović
Relja Vulanović
Affiliation:
Institute of Mathematics, University of Novi Sad, ul. Dr I Djuricica 4, Yu-21000 Novi Sad, Yugoslavia
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Abstract

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A quasilinear singularly perturbed boundary value problem whose solution has a shock layer is investigated. Estimates of the derivatives of the solution are derived. Based on these estimates, a new independent variable is introduced. Then the transformed problem is solved numerically using finite - difference schemes. The transformation corresponds to solving the original problem on a mesh which is dense in the layer. The linear convergence uniform in the perturbation parameter is proved in the discrete L1 norm. Numerical results show uniform pointwise convergence too.

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 41 , Issue 1 , February 1990 , pp. 75 - 86
Copyright
Copyright © Australian Mathematical Society 1990

References

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