Exact Difference Schemes and Difference Schemes of Arbitrary Given Degree of Accuracy for Generalized One-Dimensional Third Boundary Value Problems

Abstract

A variational problem is formulated which is a generalization of the third boundary value problem for one-dimensional equations. Conditions of existence and uniqueness of solutions are considered. The numerical approximation of arbitrary given degree of accuracy (truncated difference schemes) regarded in this paper is based on the three-point difference relations for the exact solution (exact difference scheme).