A Class of One-Dimensional Variational Inequalities and Difference Schemes of Arbitrary Given Degree of Accuracy

Abstract

A new class of one-dimensional variational inequalities with obstruction on the boundary is investigated and a theorem of existence and uniqueness of solution is proved. The investigated properties of the exact solution give an opportunity to construct the three -point difference relations for this solution (exact difference scheme). A numerical three-point approximation of arbitrary given degree of accuracy (truncated difference scheme) is proposed.