Singular perturbation problems and their numerical solutions

In this thesis, information is provided about perturbation theory and domain of influence. Additionally, singular perturbation problems and the characteristics of singular perturbation problems are emphasized. The solution of problems with delayed singularly perturbed differential equations, which have boundary layers at the left or right, has been achieved using the numerical integration method with a uniform grid. Along with the numerical integration method, the trapezoidal method, finite difference method, and Thomas algorithm were also utilized. After the implementation of the Thomas algorithm, the efficiency and accuracy of the method were demonstrated with tables and figures. The relationship between approximate solutions for different values of and was obtained using an applicable mathematical program. This thesis consists of four chapters: In the introduction, a literature review related to our study is provided. In the materials and methods section, basic definitions and theories related to the content of the thesis are presented. In the findings and discussion section, applications of examples for solving problems with delayed singularly perturbed differential equations using the numerical integration method are conducted. The fourth chapter includes the evaluation of the thesis in the conclusions and recommendations section.