Comparison of multiple-scales and numerical methods for the solution of singularly perturbed boundary layer problems

In this study, a multiple scale method is presented for solving of singularly perturbed with boundary layers problems. The original second-order singularly perturbed differential equations are transformed into partial differential equations. These problems are approximately solved by the multiple scale method and the convergence of the proposed method is tested by the finite difference method. In this thesis, the numerical method presented for the test is the exponential fitted finite difference scheme. When exponential fitted finite difference schemes are constructed, interpolation quadrature rules are used that contain the base function, which is the remaining term in integral form. The base functions are chosen to eliminate the method error. In some examples, two methods are compared with the computer program Matlab codes