Numerical method for a system of linear equations of second order with a small parameter on a semi-infinite interval

A boundary value problem for a linear system of ordinary second order differential equations with a small parameter at higher derivatives on a semi-infinite interval is considered. Systems of reaction-diffusion and convection-diffusion equations are considered. The method of reduction of a problem to a finite interval problem, based on the extraction of a set of solutions satisfying the limit conditions on infinity, is investigated. Auxiliary singular Cauchy problems for the differential matrix Riccati equations are solved with the use of a series in powers of a small parameter and an independent variable. Accuracy of the method proposed is estimated. The Shishkin mesh is proposed for solving a problem after its reduction to a finite interval. The results of numerical experiments are presented.