Differential and difference Green functions for two point second order boundary value problems

In this study, differential and difference Green?s functions for second order boundary value problems and the feature of these functions are examined. First, Green?s function and its properties were examined for self adjoint and non-self adjoint boundary value problems. Then, some aplications were given for them. In the next section, difference Green?s function and its features were analyzed for uniform and non-uniform meshes and estimates for this function were given. Some estimates for the solution of finite difference boundary value problems were obtained by using difference Green?s function. Finally, the error estimates for singularly pertürbed finite difference problem on a special non-uniform mesh was obtained by using the Green?s function and the rate of convergence was evaluated. Key Words: Green Function, Boundary Value Problem, Difference Schemes, Convection-Diffusion Problems, Singular Perturbation