Development and Application of Numerical Methods for Equations of Mixed Type in an Unbounded Domain

Abstract

We propose a generalization of methods for solving problems for a linear elliptic operator with a known fundamental solution in an unbounded domain to the case of mixed-type problems. Two new methods are constructed, the method of setting integral boundary conditions and a three-stage iterative method. The scope of the methods constructed is limited to the cases where the operators have a known fundamental solution outside some finite domain. Numerical algorithms implemented as computer software are created to solve particular problems with the methods proposed. The applicability of the methods to differential and integro-differential equations in the two-dimensional case and the possible applicability to three-dimensional problems are demonstrated.