COMPARATIVE ANALYSIS OF THE FAMILY OF NEWTON-HSSOR ITERATIVE METHODS FOR THE SOLUTION OF NONLINEAR SECOND-ORDER TWOPOINT BOUNDARY VALUE PROBLEMS

Sulaiman, J and Sunarto, Andang and Khatim Hasan, Mohd and Othman, Mohammad COMPARATIVE ANALYSIS OF THE FAMILY OF NEWTON-HSSOR ITERATIVE METHODS FOR THE SOLUTION OF NONLINEAR SECOND-ORDER TWOPOINT BOUNDARY VALUE PROBLEMS. Journal Kalam, 9 (2). pp. 18-23. ISSN 2540-7759

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Abstract

The purpose of this paper is to investigate the comparative analysis of HSSOR iteration family together with Newton scheme in solving the nonlinear systems generated from the discretization process of second order two-point nonlinear boundary value problems via The half-sweep finite difference scheme. In order to get the numerical solution of the generated nonlinear systems, firstly the Newton scheme is used to linearize the nonlinear system into the form of linear system. In addition to that, the basic formulation and implementation of the HSSOR iteration family are also shown. Consequently numerical results of these iterative methods based on three examples have been compared to demonstrate the validity and applicability of tested methods. Clearly, The findings show that the Red-Black-Newton-HSSOR method indicates the superiority over other tested methods.

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