Nabi I. Ibrahem, A., A. Ahmed, A. (2012). The Newton-Kantorovich method for Non-linear System of third order partial differential equations. , 3(3), 230-251.
Abdul Nabi I. Ibrahem; Afrah A. Ahmed. "The Newton-Kantorovich method for Non-linear System of third order partial differential equations". , 3, 3, 2012, 230-251.
Nabi I. Ibrahem, A., A. Ahmed, A. (2012). 'The Newton-Kantorovich method for Non-linear System of third order partial differential equations', , 3(3), pp. 230-251.
Nabi I. Ibrahem, A., A. Ahmed, A. The Newton-Kantorovich method for Non-linear System of third order partial differential equations. , 2012; 3(3): 230-251.

The Newton-Kantorovich method for Non-linear System of third order partial differential equations

JOURNAL OF THI-QAR SCIENCE
Article 1, Volume 3, Issue 3, 2013, Pages 230-251
Authors
Abdul Nabi I. Ibrahem; Afrah A. Ahmed
Abstract
Abstract:
In this paper we generalized Newton-Kantorovich method to be applied to a third order nonlinear system of
partial differential equations (PDEs), then we discuss the stability analysis of this method. The generalized
(N-K) is applied to the KdV (Korteweg-de Vries) equations and the general KdV system of nonlinear
equations. The numerical solutions of these two systems are obtained by using the Matlab. The numerical
results are compared with the exact solutions. We deduce that our results are fairly good approximations to
the exact solution. These facts are reported in tables and figures.
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