Nonlocal boundary value problem in terms of flow for Sturm-Liouville operator in differential and difference statements

Abstract

Sturm-Liouville operator with second kind of nonlocal boundary value conditions is considered. For the classical solution, a priori estimate is established and unique existence is proved. Associated finite-difference scheme is proposed on uniform mesh and second-order accuracy for approximation is proved. An application of obtained results to nonlocal boundary problems with weight integral conditions is provided.

Keywords

• sturm-liouville operator
• nonlocal boundary value problem
• second kind of nonlocal boundary conditions
• a priori estimate
• finite-difference scheme
• second-order of accuracy approximation