Analytic - numerical solutions with a priori error bounds for a class of strongly coupled mixed partial di erential systems

This paper deals with the construction of analytic-numerical solutions with a priori error bounds for systems of the type ut = Auxx, u(0; t) + ux(0; t) = 0, Bu(1; t) + Cux(1; t) = 0, 0¡x¡ 1; t ¿ 0, u(x; 0) = f(x). Here A, B, C are matrices for which no diagonalizable hypothesis is assumed. First an exact series solution is obtained after solving appropriate vector Sturm–Liouville-type problems. Given an admissible error and a bounded subdomain D, after appropriate truncation an approximate solution constructed in terms of data and approximate eigenvalues is given so that the error is less than the pre xed accuracy , uniformly in D. c © 1999 Elsevier Science B.V. All rights reserved.