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Application of the symmetry classification to the boundary value problem of nonlinear partial differential equations

Sudao Bilige Wang Xiao-Min Wuyun Morigen

Application of the symmetry classification to the boundary value problem of nonlinear partial differential equations

Sudao Bilige, Wang Xiao-Min, Wuyun Morigen
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Publishing process
  • Received Date:  31 August 2013
  • Accepted Date:  03 November 2013
  • Published Online:  05 February 2014

Application of the symmetry classification to the boundary value problem of nonlinear partial differential equations

  • 1. College of Sciences, Inner Mongolia University of Technology, Hohhot 010051, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant Nos. 11071159, 11261034) and the High Education Science Research Program of Inner Mongolia, China (Grant No. NJZY12056).

Abstract: In this paper, we study the application of the symmetry classification to the boundary value problem of nonli-near partial differential equations. Firstly, by using differential characteristic set algorithm for the complete symmetry classification of partial differential equations, the complete symmetry classification of a given boundary value problem of nonlinear partial differential equations is proposed. Secondly, by using an extended symmetry, the boundary value problem of nonlinear partial differential equations is reduced to an initial value problem of the original differential equations. Finally, we numerically solve the initial value problem of the original differential equations by using Runge-Kutta method.

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