Numerical Solutions of Some Differential Equations Using B-Spline Collocation Method

Abstract

Chapter 1 is introductory in nature. Besides stating some numerical techniques like Finite Difference methods, Finite Element method, Finite Volume method and methods of weighted residuals it gives an introduction to B-Spline and existing literature review. In second chapter, a numerical technique for a system of singularly perturbed boundary value problems using cubic-B-spline functions is derived. Simplicity of the adaptation of B-splines and obtaining acceptable solutions can be noted as advantages of given numerical methods. The results obtained using the proposed method are good and maximum absolute errors are negligible. In third chapter, a numerical scheme is proposed for the numerical solutions of the second order two point mixed boundary value problems based on quintic-B-spline functions.