Numerical Solutions of Nonlinear Second-Order Two-Point Boundary Value Problems Using Half-Sweep SOR With Newton Method

In this paper, we examine the performance of Half-Sweep Succesive Over-
Relaxation (HSSOR) iterative method together with Newton scheme namely
Newton-HSSOR in solving the nonlinear systems generated from second-order
�nite di�erence 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 methods are also presented. Numerical results for three test examples
have demonstrated the performance of Newton-HSSOR method compared to
other existing SOR methods