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Applied Mathematics and Mechanics (English Edition) ›› 1996, Vol. 17 ›› Issue (5): 413-421.

• 论文 • 上一篇    下一篇

A UNIFORMLY CONVERGENT DIFFERENCE SCHEME FOR THE SINGULAR PERTURBATION PROBLEM OF A HIGH ORDER ELLIPTIC DIFFERENTIAL EQUATION

刘国庆1, 苏煜城2   

  1. 1. Nanjing Institute of Chemical Technology, Nanjing 210009, P. R. China;
    2. Nanjing University, Nanjing 210008, P. R. China
  • 收稿日期:1995-04-28 出版日期:1996-05-18 发布日期:1996-05-18

A UNIFORMLY CONVERGENT DIFFERENCE SCHEME FOR THE SINGULAR PERTURBATION PROBLEM OF A HIGH ORDER ELLIPTIC DIFFERENTIAL EQUATION

Liu Guoqing1, Su Yucheng2   

  1. 1. Nanjing Institute of Chemical Technology, Nanjing 210009, P. R. China;
    2. Nanjing University, Nanjing 210008, P. R. China
  • Received:1995-04-28 Online:1996-05-18 Published:1996-05-18

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摘要： In this paper, we first consider the singularly perturbed boundary value problem for the fourth-order elliptic differential equation, establish the priori estimation of the solution of the continuous problem. Then, we present an exponential fitted difference scheme and discuss the solution properties of the difference equations. Finally, the uniform convergence of this scheme with respect to the small parameter in the discrete energy norm, is proved.

Abstract: In this paper, we first consider the singularly perturbed boundary value problem for the fourth-order elliptic differential equation, establish the priori estimation of the solution of the continuous problem. Then, we present an exponential fitted difference scheme and discuss the solution properties of the difference equations. Finally, the uniform convergence of this scheme with respect to the small parameter in the discrete energy norm, is proved.

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