A Sum-Difference Method for Constructing an Asymptotic Solution to a Boundary Value Problem of a Nonlinear Difference Equation With a Small Parameter

Abstract

Finite-difference equations proved to be a convenient mathematical model on describing impulse systems, combinatorial analysis problems, discrete analogues of mathematical physics equations, financial analysis tasks, etc. Oneshould point out that difference equations are encountered in the numerical solution of various classes of differential and integro- differential ones using the finite difference method. The article deals with methods of constructing an asymptotic solution to the boundary value problem of a system of a nonlinear difference equation with a small parameter. The problem is solved by reducing the boundary-value problem to the Cauchy problem for a system of total-difference equations with a small parameter. The efficiency of the method algorithm for the asymptotic expansion of the task of a boundary value problem in a definite example is shown.