Proceedings of the Edinburgh Mathematical Society (Series 2)

Research Article

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

L. Jódara1, E. Navarroa1 and J. A. Martina2

a1 Departamento de Matemática Aplicada, Universidad Politécnica de Valencia, P.O. Box 22012, Valencia, Spain (ljodar@mat.upv.es)

a2 Departamento de Análisis Matemático y Matemática Aplicada, Universidad de Alicante, Ap. Correos 99, E-03080 Alicante, Spain (jose.martin@ua.es)

Abstract

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.

(Received March 16 1998)

Keywords

  • coupled diffusion problem;
  • coupled boundary conditions;
  • vector boundary-value differential system;
  • analytic-numerical solution;
  • Moore–Penrose pseudoinverse