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

{ -d(2)u(t)/dt(2) + Au(t) = f(t), 0 < t < 1,

u(0) = phi, u(1) = Sigma(J)(j=1) alpha(j)u(lambda(j)) + psi, (1)

Sigma(J)(j=1)vertical bar alpha(j)vertical bar <= 1, 0 < lambda(1) < lambda(2) < ... < lambda(J) < 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 Holder spaces is established.