Quartic B – Spline Method for Solving a Singular Singularly Perturbed Third-Order Boundary Value Problems

Hradyesh Kumar Mishra^1, and Sonali saini¹

¹Department of Mathematics Jaypee University of Engineering & Technology Guna-473226(M.P) India

Cite this paper:
Hradyesh Kumar Mishra and Sonali saini. Quartic B – Spline Method for Solving a Singular Singularly Perturbed Third-Order Boundary Value Problems. American Journal of Numerical Analysis. 2015; 3(1):18-24. doi: 10.12691/ajna-3-1-3

Abstract

In this paper, we study the numerical solution of singular singularly perturbed third-order boundary value problems (BVPs) by using Quartic B-spline method. An efficient algorithm is presented here to solve the approximate solution of the given problem. To understand our method, we introduce the Quartic B-spline basis function in the form of at the different knots. After that we derive our method by using numerical difference formulas to construct the approximate values. Then we use the linear sequence of Quartic B-spline to get the numerical solution of the system of equations. These systems of equations are solved by using MATLAB. Three examples are illustrated to understand the present method.

Keywords:
Singular singularly perturbed two-point problem third-order BVPs Basis function Quartic B-spline

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