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 u"t = (b(t)/a(x))u"x"x, 0 0, a"1u(0, t) + a"2u"x(0, t) = 0, b"1u(L, t) + b"2u"x(L, t) = 0, u(x, 0) = f(x), 0 @? x @? L. Uniqueness and existence of an exact series solution are treated. Given @e > 0, t"0 > 0 andD(t"0, t"1) = {(x, t); 0 @?x @? L, t"0 @? t @? t"1} an approximate analytic-numerical solution involving only a finite number of eigenvalues is given. For this finite number of eigenvalues @l"1,..., @l"n"2, the admissible accuracy @l@l"i - \@?gl"i@l @? @d is determined so that the approximation error of the numerical solution u@?(x, t) with respect to the exact series solution is less than @e uniformly in D(t"0, t"1).