New efficient numerical methods to describe the heat transfer in a solid medium

The analysis of heat conduction through a solid with heat generation leads to a linear matrix differential equation with separated boundary conditions. We present a symmetric second order exponential integrator for the numerical integration of this problem using the imbedding formulation. An algorithm to implement this explicit method in an efficient way with respect to the computational cost of the scheme is presented. This method can also be used for nonlinear boundary value problems if the quasilinearization technique is considered. Some numerical examples illustrate the performance of this method.