Numerical solutions of nonlinear second-order two-point boundary value problems using half-sweep SOR with Newton Method - Jumat Sulaiman; M.K. Hasan; M. Othman; S.A.A. Karim (2013)
In this paper, we examine the performance of Half-Sweep Successive Over-Relaxation (HSSOR) iterative method together with Newton scheme namely Newton-HSSOR in solving the nonlinear systems generated from second order finite difference discretization of the nonlinear second-order two-point boundary value problems. As well known that to linearize nonlinear systems, the Newton scheme has been used to transform the nonlinear system into the form of linear system. Then the basic formulation and implementation of Newton-HSSOR iterative method are also presented. Numerical results for three test examples have demonstrated the performance of Newton-HSSOR method compared to other existing SOR methods.