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Applied Mathematics and Mechanics (English Edition) ›› 1999, Vol. 20 ›› Issue (8): 936-942.

• 论文 • 上一篇    

ARC-LENGTH METHOD FOR DIFFERENTIAL EQUATIONS

武际可1, 许为厚2, 丁红丽1   

  1. 1. 1Department of Mechanics and Engineering Science, Peking University, Beijing 100871, P R China;
    2. Department of Mathematics, Hong Kong University of Science and Technology, Hong Kong, P R China
  • 收稿日期:1998-04-20 修回日期:1999-02-14 出版日期:1999-08-18 发布日期:1999-08-18

ARC-LENGTH METHOD FOR DIFFERENTIAL EQUATIONS

Wu Jike1, W H Hui2, Ding Hongli1   

  1. 1. 1Department of Mechanics and Engineering Science, Peking University, Beijing 100871, P R China;
    2. Department of Mathematics, Hong Kong University of Science and Technology, Hong Kong, P R China
  • Received:1998-04-20 Revised:1999-02-14 Online:1999-08-18 Published:1999-08-18

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摘要： An arc_length method is presented to solve the ordinary differential equations(ODEs)with certain types of singularity such as stiff property or discontinuity on continuum problem. By introducing one or two arc_length parameters as variables, the differential equations with singularity are transformed into non_singularity equations, which can be solved by usual methods. The method is also applicable for partial differential equations(PDEs), because they may be changed into systems of ODEs by discretization. Two examples are given to show the accuracy, efficiency and application.

关键词: differential equation, numerical method, arc_length method, Stiff equation, Burgers’ equation

Abstract: An arc_length method is presented to solve the ordinary differential equations(ODEs)with certain types of singularity such as stiff property or discontinuity on continuum problem. By introducing one or two arc_length parameters as variables, the differential equations with singularity are transformed into non_singularity equations, which can be solved by usual methods. The method is also applicable for partial differential equations(PDEs), because they may be changed into systems of ODEs by discretization. Two examples are given to show the accuracy, efficiency and application.

Key words: differential equation, numerical method, arc_length method, Stiff equation, Burgers’ equation

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