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 (

a2 Departamento de Análisis Matemático y Matemática Aplicada, Universidad de Alicante, Ap. Correos 99, E-03080 Alicante, Spain (


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)


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