On boundary value problem for mixed type equation: asymptotic analysis and effective numerical algorithm
This article is devoted to the singularly perturbed boundary value problem for elliptic-parabolic equation. The first part of this work consists in asymptotic analysis of the solution. We use the boundary function method and its modification for mixed type equations with small parameters by the higher derivatives. In the second part we create numerical algorithm based on the structure of solution under small values of parameter. We use the idea of approximate factorization of elliptic operator to the product of two parabolic operators. The aim of this work is to create an effective numerical algorithm on the base of asymptotic solution.