Abstarct: In this thesis, the B-spline method is used for the numerical solution class linear and non-linear singular boundary value problems, linear system of second-order boundary value problems and linear and non-linear singular initial value problems. The original differential equation is modified at singular point then the modified problem is solved by B-spline method. In the case of non-linear problems, we first linearize the equation using Quasilinearization technique and the resulting problem is solved by B-spline. In the present examples, the results obtained by the present method are compared with exact solution and or the another methods solution for instance: the homotopy method, the finite difference method.