The Numerical Solution of the TVD Runge-Kutta and WENO Scheme to the FPK Equations to Nonlinear System of One-Dimension
Applied and Computational Mathematics
Volume 5, Issue 3, June 2016, Pages: 160-164
Received: Jun. 19, 2016; Accepted: Jun. 27, 2016; Published: Jul. 23, 2016
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Authors
Wang Wenjie, School of Science of Chang’an University, Xi’an, China
Feng Jianhu, School of Science of Chang’an University, Xi’an, China
Xu Wei, School of Science of Northwestern Polytechnic University, Xi’an, China
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Abstract
Firstly, it was studied to the Fokker-Planck-Kolmogorov (FPK) equations for nonlinear stochastic dynamic system. Secondly, it was discussed to the third-order TVD Runge-Kutta difference scheme totime for differitial equations and the fifth-order WENO scheme for differitial operators. And combined he third-order TVD Runge-Kutta difference scheme with the fifth-order WENO scheme, obtained the numerical solution for FPK equations using the TVD Runge-Kutta WENO scheme. Finally, the numerical solution was compared with the analytic solution for FPK equations. The numerical method is shown to give accurate results and overcomes the difficulties of other methods, such as: the big value of probability density function at tail etc.
Keywords
Nonlinear System, FPK Equations, The Finite Difference Method, The TVD Runge-Kutta Scheme, The ENO Scheme, The WENO Scheme
To cite this article
Wang Wenjie, Feng Jianhu, Xu Wei, The Numerical Solution of the TVD Runge-Kutta and WENO Scheme to the FPK Equations to Nonlinear System of One-Dimension, Applied and Computational Mathematics. Vol. 5, No. 3, 2016, pp. 160-164. doi: 10.11648/j.acm.20160503.20
Copyright
Copyright © 2016 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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