On the Possibility of a Numerical Solution of the Heat and Mass Transfer Problem with the Combined Matrix&Generalized Powers of Bers Method

Abstract

Some possibilities for the combined use of the matrix method and the method of generalized powers of Bers for the numerical solution of the heat and mass transfer problem is considered. Initially, the matrix method under consideration was used by us for the analytical solution of the problem of heat and mass transfer in a homogeneous or multilayered medium with translation, axial or central symmetry for an arbitrary number of layers. Simulation is reduced to the sequential multiplication of second-order functional matrices whose components at each point are determined by the physical and geometric parameters of the current layer. The main advantage of the matrix method is that it can be used for any number of layers. It is this property of the method that makes it possible to consider of its application as a numerical one if the medium is artificially splitted into many layers.For modelling, the problem of one-dimensional diffusion of minority charge carriers generated by a wide electron beam in a semiconductor material was taken. The relative error in the computations was estimated by a uniform norm in comparison with the analytical solution. The errors made were from 0.8% to 2.9%.