Numerical solutions of singularly perturbed reaction-difussion type problem

In this thesis, we studied boundary value problems for singularly perturbed second order differential equation of reaction-diffusion type. Firstly, the problem in the linear state, then the non-linear (semi-linear) problem and finally the problem of lineer with delay are discussed. In all three classes of equations, firstly the properties of the continuous problem were given, then finite difference schemes were constructed with the help of perturbation theory and quadrature formulas. For each of these problems, difference schemes based on the appropriate Numerov method are given. The stability of the difference schemes were examined and error analyzes were performed. All these theoretical studies are supported by literature examples and numerical results are presented in tables with some solution curves.