Wu Jike, W H Hui, Ding Hongli. Arc-Length Method for Differential Equations[J]. Applied Mathematics and Mechanics, 1999, 20(8): 875-880.
Citation: Wu Jike, W H Hui, Ding Hongli. Arc-Length Method for Differential Equations[J]. Applied Mathematics and Mechanics, 1999, 20(8): 875-880.

Arc-Length Method for Differential Equations

  • Received Date: 1998-04-20
  • Rev Recd Date: 1999-02-14
  • Publish Date: 1999-08-15
  • A kind arc-length method is presented to solve the ordinary differential equations(ODEs) with certain types of singularit y 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.
  • loading
  • [1]
    Riks E.An incremental approach to the solution of snapping and buckling problems[J].Int J Solid Structures,1979,15(4):529~551.
    [2]
    武际可,周.高维Hopf分叉的数值计算[J].北京大学学报(自然科学版),1993,29(5):574~582.
    [3]
    Hui W H.Generalized L agrangian formulation of computational fluid dynamics[A].In:M Hafez,K Oshima Eds.Computational Fluid Dynamics Review,[C].Hong Kong:Wiley,1995.
    [4]
    Hairer E,et al.Solvin g Ordinary Differential Equations Ⅱ,Stiff and Differential-Algebraic Problems[M].Berlin,Heidelberg,New York:Springer-Verlag,1991.
    [5]
    Schulz-Rinne C W.The Riemann problem for two-dimensional gas dynamics and new limiters for high-order schemes[D].Ph Ddissertation.Swiss:the Swiss Federal Institute of Technology Zurich,1993.
    [6]
    苏先樾.旋转壳非线性分析[D].博士论文.北京:北京大学,1985.
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (2696) PDF downloads(928) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return