Analytic-numerical solutions of diffusion mathematical models with delays

This work deals with the construction of analytic-numerical solutions of mixed problems for diffusion and reaction-diffusion equations with delay. Using the method of separation of variables, exact theoretical infinite series solutions are derived. Bounds on the truncation errors, when these series are approximated by finite sums, are given, thus providing constructive continuous numerical solutions with prescribed accuracy in bounded domains. In order to improve the computational efficiency of these numerical solutions, polynomial approximations to the initial functions are also considered.