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 ∈ > 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 |λi - λi| ≤δ is determined so that the approximation error of the numerical solution u(x,t) with respect to the exact series solution is less than ∈ uniformly in D(t0,t1).