Mixed problems for separate variable coefficient diffusion equations: The non-dirichlet case approximate solutions with a priori error bounds

This paper deals with the construction of accurate analytic-numerical solutions of non-Dirichlet mixed variable coefficient diffusion problems of the type ut = (b(t)/a(x))uxx, 0 < x < L, t > 0, a1u(0, t) + a2ux(0, t) = 0, b1u(L, t) + b2ux(L, t) = 0, u(x, 0) = f(x), 0 ≤ x ≤ L. Uniqueness and existence of an exact series solution are treated. Given ϵ > 0, t0 > 0 and D(t0, t1) = {(x, t); 0 ≤x ≤ L, t0 ≤ t ≤ t1} an approximate analytic-numerical solution involving only a finite number of eigenvalues is given. For this finite number of eigenvalues λ1,…, λn2, the admissible accuracy λλi − \̃gliλ ≤ δ is determined so that the approximation error of the numerical solution ũ(x, t) with respect to the exact series solution is less than ϵ uniformly in D(t0, t1).