Quarter-Sweep Gauss-Seidel Method with Quadratic Spline Scheme applied to Fourth Order Two-Point Boundary Value Problems

摘要

The aim of this paper is to describe the application of Quarter-Sweep Gauss-Seidel (QSGS) iterative method using quadratic spline scheme for solving fourth order two-point linear boundary value problems. In the line to derive approximation equations, firstly the fourth order problems need to be reduced onto a system of second-order two-point boundary value problems. Then two linear systems have been constructed via discretization process by using the corresponding quarter-sweep quadratic spline approximation equations. The generated linear systems have been solved using the proposed QSGS iterative method to show the superiority over Full-Sweep Gauss-Seidel (FSGS) and Half-Sweep Gauss-Seidel (HSGS) methods. Computational results are provided to illustrate that the effectiveness of the proposed QSGS method is more superior in terms of computational time and number of iterations as compared to other tested methods.