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A Wavelet Method for Solving Nonlinear Time-Dependent Partial Differential Equations

Xiaojing Liu1, Jizeng Wang1,2, Youhe Zhou1,2
Key Laboratory of Mechanics on Disaster and Environment in Western China, the Ministry of Education.
School of Civil Engineering and Mechanics, Lanzhou University, Lanzhou, Gansu 730000, China.
Corresponding author. Email: jzwang@lzu.edu.cn (J. Wang); zhouyh@lzu.edu.cn (Y. Zhou).

Computer Modeling in Engineering & Sciences 2013, 94(3), 225-238. https://doi.org/10.32604/cmes.2013.094.225

Abstract

A wavelet method is proposed for solving a class of nonlinear timedependent partial differential equations. Following this method, the nonlinear equations are first transformed into a system of ordinary differential equations by using the modified wavelet Galerkin method recently developed by the authors. Then, the classical fourth-order explicit Runge-Kutta method is employed to solve the resulting system of ordinary differential equations. To justify the present method, the coupled viscous Burgers’ equations are solved as examples, results demonstrate that the proposed wavelet algorithm have a much better accuracy and efficiency than many existing numerical methods, and the order of convergence of such a wavelet method can even reach about 5.

Keywords

modified wavelet Galerkin method, Runge-Kutta method, nonlinear time-dependent partial differential equations, Burgers’ equation

Cite This Article

Liu, X., Wang, J., Zhou, Y. (2013). A Wavelet Method for Solving Nonlinear Time-Dependent Partial Differential Equations. CMES-Computer Modeling in Engineering & Sciences, 94(3), 225–238.

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This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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