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Exact and analytic-numerical solutions of strongly coupled mixed diffusion problems

Published online by Cambridge University Press:  20 January 2009

L. Jódar ,
E. Navarro  and
J. A. Martin
L. Jódar
Affiliation:
Departamento de Matemática Aplicada, Universidad Politécnica de Valencia, P.O. Box 22012, Valencia, Spain ([email protected])
E. Navarro
Affiliation:
Departamento de Matemática Aplicada, Universidad Politécnica de Valencia, P.O. Box 22012, Valencia, Spain ([email protected])
J. A. Martin
Affiliation:
Departamento de Análisis Matemático y Matemática Aplicada, Universidad de Alicante, Ap. Correos 99, E-03080 Alicante, Spain ([email protected])
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Abstract

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This paper deals with the construction of exact and analytical-numerical solutions with a priori error bounds for systems of the type ut = Auxx, A1u(0, t) + B1ux (0, t) = 0, A2u (1, t) + B2ux (1, t) = 0, 0 < x < 1, t > 0, u(x, 0) = f(x), where A1, A2, B1 and B2 are matrices for which no simultaneous diagonalizable hypothesis is assumed, and A is a positive stable matrix. Given an admissible error ε and a bounded subdomain D, an approximate solution whose error with respect to an exact series solution is less than ε uniformly in D is constructed.

Keywords

coupled diffusion problemcoupled boundary conditionsvector boundary-value differential systemanalytic-numerical solutionMoore–Penrose pseudoinverse
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 43 , Issue 2 , June 2000 , pp. 269 - 293
Copyright
Copyright © Edinburgh Mathematical Society 2000

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