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eigenvalue inequality

Proceedings of the Edinburgh Mathematical Society (1)

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ANALYTIC–NUMERICAL SOLUTIONS WITH A PRIORI BOUNDS FOR MATRIX–VECTOR PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS
Lucas Jódar, Marco Marletta
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 45 / Issue 1 / February 2002

Published online by Cambridge University Press:

05 February 2002, pp. 5-25
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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