A New Method to Solve a Non Linear Differential System
Commenced in January 2007
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Edition: International
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A New Method to Solve a Non Linear Differential System

Authors: Seifedine Kadry

Abstract:

In this article, our objective is the analysis of the resolution of non-linear differential systems by combining Newton and Continuation (N-C) method. The iterative numerical methods converge where the initial condition is chosen close to the exact solution. The question of choosing the initial condition is answered by N-C method.

Keywords: Continuation Method, Newton Method, Finite Difference Method, Numerical Analysis and Non-Linear partial Differential Equation.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1075150

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References:


[1] E. Allgower, Introduction to Numerical Continuation methods. SIAM 2003, ch. 2, 12.
[2] W. Govaerts, Numerical methods for Bifurcations of Dynamical Equilibrium, SIAM. 2000.
[3] J. Rappaz et M. Picasso, Introduction ├á l'analyse numérique. 2001, pp 119-127.
[4] J.M. Ortega and W.C. Rheinboldt (1970), Iterative solution of non-linear equations.
[5] W.C. Rheinboldt (1974), Methods for solving systems of non-linear equations.
[6] S. Kadry, A new algorithm for the partition of interval for the continuation method. Proceeding ICAM 2005.
[7] S. Kadry and N. Nassif, New algorithm for nonlinear method, master's thesis 2001, ch. 3,4.
[8] G. Evans (2000), Numerical methods for PDE.
[9] A. Quarteron, Numerical mathematics.2204, Ch. 7.
[10] A. Chateauneuf, Comprendre les elements finis.2005