Finite difference schemes for inverse elliptic problems with nonlocal boundary value conditions

In this thesis, the multi_point nonlocal boundary conditional inverse problem is investigated in a Hilbert space. For the approximate solution of the inverse elliptic problem, third and fourth order accuracy difference schemes are established. Stability, almost coercive stability and coercive stability estimates are obtained for the solutions of the presented difference schemes. The operator method is used to prove the stability inequalities. For the approximate solution of the inverse nonlocal boundary value problems for the multidimensional partial elliptic differential equation, third and fourth order accuracy difference schemes are created. For the approximate solution of nonlocal inverse Dirichlet and Neumann type boundary value problems for multidimensional partial elliptic difference equations, higher order accuracy difference schemes are established. Stability estimates for solutions of difference schemes are discussed. In order to find numerical solutions of third and fourth order accuracy difference schemes, examples tested by MATLAB codes are given together with the algorithm.