WELL-POSEDNESS OF A NONLOCAL BOUNDARY VALUE DIFFERENCE ELLIPTIC PROBLEM

The second order of approximation two-step difference scheme for the numerical solution of a nonlocal boundary value problem for the elliptic differential equation-v ''(t)+Av(t)=f(t)(0 <= t <= T),v(0)=v(T)+phi,integral 0Tv(s)ds=psi in an arbitrary Banach space E with the positive operator A is presented. The well-posedness of the difference scheme in Banach spaces is established. In applications, the stability, almost coercive stability and coercive stability estimates in maximum norm in one variable for the solutions of difference schemes for numerical solution of two type elliptic problems are obtained.