MKSOR iterative method with cubic b-spline approximation for solving two-point boundary value problems

Abstract

In this study, two-point boundary value problems have been discretized by using cubic B-spline discretization scheme to derive the cubic B-spline approximation equations that corresponds. Then, this approximation equation is used to develop system of cubic B-spline approximation equations. To get the numerical solutions, there are three iterative methods such as Gauss-Seidel (GS), Successive Over Relaxation (SOR) and Modified Kaudd Successive Over Relaxation (MKSOR) used to solve the generated systems of linear equations. For the purpose of comparison, the GS iterative method has been designated as a control method for the SOR and MKSOR iterative methods. Three examples of problems also have been considered to test the effectiveness of these proposed iterative methods. From the numerical results, MKSOR iterative method is superior method in terms of number of iterations and computational time.

Keywords: cubic B-spline approximation; two-point boundary value problem; MKSOR iteration