High order of accuracy stable difference schemes for the approximate solution of the multipoint NBVP for the hyperbolic equation

Abstract

The abstract multipoint nonlocal boundary value problem (NBVP) {d2u(t)dt2+Au(t) = f(t)0≤t≥T,u(0) = ∑ r = 1nαru(λr)+φ,ut(0) = ∑ r = 1nβrut(λr)+ψ,0<λ1<λ2<...<λn≤1 for the hyperbolic equation in a Hilbert space H with the self-adjoint positive definite operator A is considered. The third and fourth order of accuracy difference schemes for approximate solutions of this problem are presented. The stability estimates for solutions of these difference schemes are obtained and the results of numerical experiments are presented in order to verify theoretical statements.