International Journal of Mathematics and Computational Science
Articles Information
International Journal of Mathematics and Computational Science, Vol.2, No.2, Apr. 2016, Pub. Date: May 12, 2016
Construction of Analytic Solution for Coupled Cubic Nonlinear Systems Using Homotopy Analysis Method
Pages: 43-54 Views: 732 Downloads: 502
Authors
[01] J. M. Guo, College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua, Zhejiang, P. R. China.
[02] Y. H. Qian, College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua, Zhejiang, P. R. China.
[03] S. P. Chen, College of Mathematics, Xiamen University of Technology, Xiamen, P. R. China.
Abstract
In this paper, the existence solution of initial value problem for coupled cubic nonlinear systems is proved at first. Then by using the homotopy analysis method (HAM), an analytical approximation of those systems can be obtained. It is full of freedom to choose a set of base functions when using the HAM, and as the set of base functions is chosen differently, the analytical approximation solutions which will have some different effect. Therefore, it is an interesting and meaningful task to get a more efficient analytical approximation by a better set of base functions. Furtherly, by combining the HAM with padé approximation, the result can be obtained on broader region of convergence. To illustrate the accuracy of the present method, the solutions obtained in this paper are compared with those of Runge-Kutta method, which shows the HAM is effective and feasible.
Keywords
Initial Value Problem, Coupled Cubic Nonlinear Systems, the Homotopy Analysis Method, Homotopy Padé Approximation
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