Quintic B-Spline Method for Singularly Perturbed Fourth-Order Ordinary Differential Equations of Reaction–Diffusion Type

A quintic B-spline method has been proposed in this paper for the numerical solution of fourth order singularly perturbed two-point boundary value problems of reaction–diffusion type. Such types of problems arise in various fields of science and engineering, such as electrical network and vibration problems with large Peclet numbers, Navier–Stokes flows with large Reynolds numbers in the theory of hydrodynamics stability, reaction–diffusion process, quantum mechanics and optimal control theory etc. These types of problems are very important physically and difficult to solve because of boundary layers lies at the end point of domain. This method is directly applied to the problem without reducing the order of differential equation. The convergence analysis of the present method is also given and it has been proved to be of second order. The proposed method is applied on two numerical examples which verify theoretical estimates and numerical results are compared with the existing method. The numerical results are calculated with the help of MATLAB software.