%P 69-75
%C Kuala Lumpur
%T Fourth-order solutions of nonlinear two-point boundary value problems by Newton-HSSOR iteration
%I American Institute of Physics Inc.
%V 1602
%A J. Sulaiman
%A M.K. Hasan
%A M. Othman
%A S.A.A. Karim
%D 2014
%R 10.1063/1.4882468
%O cited By 7; Conference of 3rd International Conference on Mathematical Sciences, ICMS 2013 ; Conference Date: 17 December 2013 Through 19 December 2013; Conference Code:106205
%J AIP Conference Proceedings
%L scholars5152
%X In this paper, the Half-Sweep Successive Over-Relaxation (HSSOR) iterative method together with Newton scheme namely Newton-HSSOR is investigated in solving the nonlinear systems generated from the fourth-order half-sweep finite difference approximation equation for nonlinear two-point boundary value problems. The Newton scheme is proposed to linearize the nonlinear system into the form of linear system. On top of that, we also present the basic formulation and implementation of Newton-HSSOR iterative method. For comparison purpose, combinations between the Full-Sweep Gauss-Seidel (FSGS) and Full-Sweep Successive Over-Relaxation (FSSOR) iterative methods with Newton scheme, which are indicated as Newton-FSGS and Newton-FSSOR methods respectively have been implemented numerically. Numerical experiments of two problems are given to illustrate that the Newton-HSSOR method is more superior compared with the tested methods. © 2014 AIP Publishing LLC.
%K Boundary value problems; Linear systems; Nonlinear equations; Nonlinear systems; Numerical methods, Basic formulation; Finite difference approximations; Fourth-order scheme; Gauss-Seidel; Numerical experiments; SOR iteration; Successive over relaxation; Two-point boundary value problem, Iterative methods