Numerical Method for Three-Point Vector Difference Schemes on Infinite Interval

Abstract

A three-point vector difference scheme on a infinite interval is considered. Method of reduction of this scheme to a scheme with a finite number of nodes is proposed. Method is based on the extraction of sets of solutions of the difference equation, satisfying the limiting conditions at infinity. The method is applied for numerical solution of an elliptic singularly perturbed problem in a strip. Results of numerical experiments are discussed.