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ANALYTIC–NUMERICAL SOLUTIONS WITH A PRIORI BOUNDS FOR MATRIX–VECTOR PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS
Published online by Cambridge University Press: 05 February 2002
Abstract
We consider a parabolic matrix–vector system in which the diffusion matrix may be time dependent. For the time-independent case we construct approximate solutions with guaranteed error bounds using spectral information from certain matrix–vector Sturm–Liouville problems. For the time-dependent case we employ an approximation procedure which reduces the problem, on each time-step, to the time-independent case. We give an algorithm which may be used a priori at each time-step in the time-dependent case to guarantee accuracy to a specified tolerance.
AMS 2000 Mathematics subject classification: Primary 35C10; 35M10. Secondary 15A
- Type
- Research Article
- Information
- Proceedings of the Edinburgh Mathematical Society , Volume 45 , Issue 1 , February 2002 , pp. 5 - 25
- Copyright
- Copyright © Edinburgh Mathematical Society 2002
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