Nonlocal boundary value problem in terms of flow for Sturm-Liouville operator in differential and difference statements
Authors: Dovlet M. Dovletov
Journal: e-Journal of Analysis and Applied Mathematics (e-JAAM), e-ISSN 2544-9990
Volume: 2018 · Pages: 37 - 55
Published Online: 25 Jul 2019
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