Exact and analytic numerical solution of coupled parabolic mixed problems in a semi-infinite medium

This paper deals with the construction of accurate analytic-numerical approximations of coupled parabolic mixed systems. Using sine Fourier transforms, an exact expression of the exact solution is given. Then, given an admissible error e and a time bounded subdomain Ω an analytic numerical solution is constructed so that the approximation error is less than e in Ω.