Quintic non-polynomial spline methods for third order singularly perturbed boundary value problems

In this paper, the non-polynomial spline function is used to find the numerical solution of the third order singularly perturbed boundary value problems of the reaction-diffusion equation type. The convergence analysis is discussed and the method is shown to have fourth order convergence. To validate the applicability of the method, two model examples have been solved for different values of the perturbation parameter and mesh sizes. The numerical results have been tabulated and also presented in graphs. It can be observed from the results that the present method approximates the exact solution very well.