Source identification problem with multi point nonlocal boundary condition for parabolic equation

In this study, the multi-point non-local boundary value identification problem for parabolic equations was investigated. The existence of the solution of the problem and the stability estimates were investigated. In finding the approximate solution of the identification problem, first and second order finite difference schemes have been established. Then, stability estimates were obtained for the solution of these difference schemes. After obtaining the abstract results, the stability of the solution of the identification problem for the multidimensional parabolic partial differential equation given by Dirichlet conditions was examined. For this problem, both first and second order difference schemes were established and stability analysis was performed. In addition, algorithm and MATLAB codes are presented in the test samples to find the solution of the multi-point parabolic identification boundary value problem.