In this paper, we consider the Newton-iterative method for solving weakly nonlinear finite-difference systems of the form F(u)=Au+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.

On solving a special class of weakly nonlinear finite-difference systems / Galligani, Emanuele. - In: INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS. - ISSN 0020-7160. - STAMPA. - 86:(2009), pp. 503-522.

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

GALLIGANI, Emanuele
2009-01-01

Abstract

In this paper, we consider the Newton-iterative method for solving weakly nonlinear finite-difference systems of the form F(u)=Au+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.
86
503
522
On solving a special class of weakly nonlinear finite-difference systems / Galligani, Emanuele. - In: INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS. - ISSN 0020-7160. - STAMPA. - 86:(2009), pp. 503-522.
Galligani, Emanuele
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/452954
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