On the Fourth Order of Accuracy Difference Scheme for the Bitsadze-Samarskii Type Nonlocal Boundary Value Problem

Abstract

The Bitsadze‐Samarskii type nonlocal boundary value problem {−d2u(t)dt2+Au(t) = f(t), 0<t<1,u(0) = φ, u(1) = ∑ j = 1Jαju(λj)+ψ, ∑ j = 1J|αj|≤1, 0<λ1<λ2<⋯<λJ<1 for the differential equation in a Hilbert space H with the self‐adjoint positive definite operator A is considered. The fourth order of accuracy difference scheme for approximate solution of the problem is presented. The well posedness of this difference scheme in difference analogue of Hölder spaces is established.