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

Abstract

In this communication, we have studied an efficient numerical approach based on uniform mesh for the numerical solutions of fourth order singular perturbation boundary value problems. Such type of problems arises in various fields of science and engineering, like 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. In the present study, a quintic B-spline method has been discussed for the approximate solution of the fourth order singular perturbation boundary value problems. The convergence analysis is also carried out and the method is shown to have convergence 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. (2010): 65L10. Keywords: Fourth order singular perturbation boundary value problem, quintic B-spline, quasilinearization, uniform mesh, convergence analysis. y (a) = η 1 , y (b) = η 2 , y (a) = η 3 , y (b) = η 4 . Mathematics Subject Classification(1.2) where η 1 , η 2 , η 3 and η 4 are finite real constants and ε is a small positive parameter, such that 0 < ε 1. Moreover, we assume that the functions p (t) ,q (t) ,r (t) and f (t) are sufficiently smooth. Further, the problem (1.1) is called non-turning point problem if p (t) ≥ α > 0 throughout the interval [a, b], where α is some positive constant and boundary layer will be in the neighbourhood of t = a [9]. In the same

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Quartic B-Spline Method for Non-Linear Second Order Singularly Perturbed Delay Differential Equations

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