High degree b-spline solution for singularly perturbed boundary value problem

Abstract

This study deals with the singularly perturbed boundary value problems. It is veryactive filed now a days, especially with improvement technology of the computermachine which is help us to do million and million of mathematical operations. Theperturbation theory benefits from this improvement to solve the boundary valueproblems, this kind of a applications can help us to solve a lot of problems occur inmany areas of engineering and applied mathematics such as fluid mechanics, quantummechanics, optimal control, chemical reactor theory, aerodynamics, reaction-diffusionprocess, geophysics, heat transport problems with large Peclet number and Navier-Strokes flows with large Reynolds numbers etc.Perturbation theory comprises mathematical methods that are used to find anapproximation solution to a problem which cannot be solved exactly, by starting fromthe exact solution to a related problem. Perturbation theory is applicable if the problemat hand can be formulated by adding a `small` term to the mathematical description ofthe exactly solvable problem.The study focuses on the some methods that solved this kind of the problems, the newscheme was used to apply the high degree b-spline interpolation, the result comparedwith the published methods recently.Keywords: Perturbation theory, B-spline Interpolation, Finite Deference Method,Shooting Method.