A New Method to Solve a Non Linear Differential System
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.
[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
[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
@article{"International Journal of Engineering, Mathematical and Physical Sciences:59450", author = "Seifedine Kadry", title = "A New Method to Solve a Non Linear Differential System ", 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.", volume = "1", number = "1", pages = "111-5", }