Approximations for Burgers equations with C-N scheme and RBF collocation methods

Volume 9, Issue 6, pp 3727--3734 http://dx.doi.org/10.22436/jnsa.009.06.23

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Authors

Huantian Xie - School of Science, Linyi University, Linyi 276005, P. R. China. Jianwei Zhou - School of Science, Linyi University, Linyi 276005, P. R. China. Ziwu Jiang - School of Science, Linyi University, Linyi 276005, P. R. China. Xiaoyi Guo - School of Science, Linyi University, Linyi 276005, P. R. China.

Abstract

The Burgers' equation is one of the typical nonlinear evolutionary partial differential equations. In this paper, a mesh-free method is proposed to solve the Burgers' equation using the finite difference and collocation methods. With the temporal discretization of the equation using C-N scheme, the solution is approximated spatially by Radial Basis Function (RBF). The numerical results of two different examples indicate the high accuracy and flexibility of the presented method.

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Keywords

• Burgers' equation
• collocation
• Crank-Nicholson (C-N) scheme
• multiquadric (MQ).

MSC

•  35L72
•  65N35

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