Quintic B-spline method for numerical solution of fourth order singular perturbation boundary value problems

Abstract

In this communication, we have studied an ecient numerical ap- proach based on uniform mesh for the numerical solutions of fourth order singular perturbation boundary value problems. Such type of problems arises in various elds of science and engineering, such as electrical network and vi- bration problems with large Peclet numbers, Navier-Stokes ows with large Reynolds numbers in the theory of hydrodynamics stability, reaction-diusion process, quantum mechanics and optimal control theory etc. In the present study, a quintic B-spline method has been discussed for the approximate solu- tion of the fourth order singular perturbation boundary value problems. The convergence analysis is also carried out and the method is shown to have con- vergence of second order. The performance of present method is shown through some numerical tests. The numerical results are compared with other existing method available in the literature.