Subject |
Local and nonlocal boundary value problems for partial differential equations |
Title |
A note on the numerical solution of the semilinear elliptic equation |
Author(s) |
Elif Ozturk, Esra Demirel |
Keywords |
semilinear elliptic equation, difference scheme, Bitsadze- Samarskii type problem |
Abstract |
The study of boundary value problems for elliptic eqautions were considered in [1-6]. A. V Bitsadze and A. A. Samarskii had proved existence and uniqueness of a classical solution to an elliptic second-order equation in a rectangle with nonlocal boundary conditions [7]. Previously, the Bitsadze-Samarskii type nonlocal boundary value problems for semilinear elliptic equations were studied [3]. The unique solvability of Bitsadze-Samarskii type nonlocal boundary value problems for the semilinear elliptic equations in a Hilbert space was investigated in that work. In this paper, we consider the same problem for approximately solving of this problem in a Hilbert Space [3] . The difference scheme is used to overcome the difficulties in numerical procedure. |