Applied Mathematics and Mechanics (English Edition) ›› 2000, Vol. 21 ›› Issue (12): 1423-1431.

• 论文 • 上一篇    下一篇

TWO TYPES OF NEW ALGORITHMS FOR FINDING EXPLICIT ANALYTICAL SOLUTIONS OF NONLINEAR DIFFERENTIAL EQUATIONS

张鸿庆, 闫振亚   

  1. Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, P. R. China
  • 收稿日期:2000-01-14 修回日期:2000-08-21 出版日期:2000-12-18 发布日期:2000-12-18
  • 基金资助:

    the National Basic Research Program Foundation of China(G1998030600);Doctoral Foundation of Education Committee of China(98014119)

TWO TYPES OF NEW ALGORITHMS FOR FINDING EXPLICIT ANALYTICAL SOLUTIONS OF NONLINEAR DIFFERENTIAL EQUATIONS

ZHANG Hong-qing, YAN Zhen-ya   

  1. Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, P. R. China
  • Received:2000-01-14 Revised:2000-08-21 Online:2000-12-18 Published:2000-12-18
  • Supported by:

    the National Basic Research Program Foundation of China(G1998030600);Doctoral Foundation of Education Committee of China(98014119)

摘要: The idea of AC=BD was applied to solve the nonlinear differential equations. Suppose that Au=0 is a given equation to be solved and Dv=0 is an equation to be easily solved. If the transformation u=Cv is obtained so that v satisfies Dv=0,then the solutions for Au=0 can be found. In order to illustrate this approach, several examples about the transformation C are given.

Abstract: The idea of AC=BD was applied to solve the nonlinear differential equations. Suppose that Au=0 is a given equation to be solved and Dv=0 is an equation to be easily solved. If the transformation u=Cv is obtained so that v satisfies Dv=0,then the solutions for Au=0 can be found. In order to illustrate this approach, several examples about the transformation C are given.

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