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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

Lucas Jódar  and
Marco Marletta
Lucas Jódar
Affiliation:
Departamento de Matemática Aplicada, Universidad Politécnica de Valencia, PO Box 22.012, 46071 Valencia, Spain
Marco Marletta
Affiliation:
Department of Mathematics and Computer Science, University of Leicester, University Road, Leicester LE1 7RH, UK
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Abstract

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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

Keywords

Sturm–Liouville problemeigenfunctioneigenvalue inequalitycomputable a priori error bounds
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