On solving a special class of weakly nonlinear finite-difference systems

Abstract

In this paper, we consider the Newton-iterative method for solving weakly nonlinear finite-difference systems of the form F ( u )=A u + G ( u )=0, where the jacobian matrix G′( u ) satisfies an affine invariant Lipschitz condition. We also consider a modification of the method for which we can improve the likelihood of convergence from initial approximations that may be outside the attraction ball of the Newton-iterative method. We analyse the convergence of this damped method in the framework of the line search strategy. Numerical experiments on a diffusion–convection problem show the effectiveness of the method.

Keywords:

• weakly nonlinear systems
• Newton-iterative method
• line search technique
• finite difference

AMS Classification :

• 65H10
• 65H20
• 65N06

C.R. Categories :

• G.1.5
• G.1.8

Acknowledgements

This research was supported by the Italian Ministry of Education, University and Research (MIUR), FIRB Project RBAU01877P.