Exact and analytic-numerical solutions of strongly coupled mixed diffusionproblems

This paper deals with the construction of exact and analytical-numerical so lutions with a priori error bounds for systems of the type u(t) = Au-xx A(1 )u(0, t)+ B(1)u(x) (0, t) = 0, A(2)u(1, t) +B(2)u(x) (1, t) = 0, 0 < x < 1, t > 0, u(x, 0) = f(x), where A(1), A(2), B-1 and B-2 are matrices for whic h no simultaneous diagonalizable hypothesis is assumed, and A is a positive stable matrix. Given an admissible error epsilon and a bounded subdomain D , an approximate solution whose error with respect to an exact series solut ion is less than epsilon uniformly in D is constructed.