| Abstract |
In the literature, the problem of Bitsadze-Samarskii type is often referred to as the boundary value problem with Bitsadze-Samarskii condition (see [2], [4] and [7]). Previously, the Bitsadze-Samarskii type nonlocal boundary value problems for linear elliptic equations were studied ([5]). In this paper, the Bitsadze-Samarskii type nonlocal boundary value problems for semilinear elliptic equations
{<K1.1/>┊
-((d²u(t))/(dt²))+Au(t)=f(t,u(t)),0
in a Hilbert space H with the self-adjoint positive definite operator A is considered. The first and second orders of accuracy difference schemes approximately solving these problems are studied. A procedure of modified Gauss elimination method is used for solving these difference schemes for the two-dimensional elliptic differential equation. The method is illustrated by numerical examples. The converge estimates for the solution of these difference schemes are obtained. |
