Uniform convergence numerical methods for solving singularly perturbed boundary value problem with integral boundary condition

This thesis consists of seven chapters. In the first and second part of the thesis, historical development of the problems and literature are given. In the third part, the materials and methods to be used in this thesis are mentioned. In the fourth part, the method to be used for the solution of the boundary value problems, some basic definitions, auxiliary theorems and theorems which are basic knowledge are given. In the fifth chapter of the study, a uniform numerical approach is given to solve the boundary value problem with singular perturbation type of reaction-diffusion type. First, explicit boundaries for the solution and the derivative of the problem were established. Then, the difference scheme in the uniform mesh is established. Uniform convergence of these difference schemes according to the perturbation parameter at the discrete maximum norm is proved. In addition, the effectiveness of the method is shown on several examples. In the sixth chapter of this thesis, similar to four the estimates in section five uniform convergence numerical methods are presented for the solution of the boundary value problem with singular perturbation with integral boundary condition. In the last part of this thesis, discussion and conclusions about our studies are given. Key words: Error estimates, Exponential finite difference scheme, Singular perturbation problems, Uniform convergence.