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Applied Mathematics and Mechanics

, Volume 12, Issue 10, pp 943–966 | Cite as

Numerical solution of singular perturbation problems for the fourth-order elliptic differential equations

  • Su Yu-cheng
  • Liu Guo-qing
Article

Abstract

In this paper we construct the finite-difference scheme for the singularly perturbed boundary value problem for the fourth-order elliptic differential equation on the basis of paper [1], and prove the uniform convergence of this scheme with respect to the small parameter ε in the discrete energy norm. Finally, we give a numerical example.

Key words

elliptic singular perturbation energy norm numerical solution 

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References

  1. [1]
    Su Yu-cheng and Liu Guo-qing, Asymptotic solution of singular perturbation problems for the fourth-order elliptic differential equations,Appl. Math. and Mech.,11, 7 (1990), 637–650.MATHMathSciNetCrossRefGoogle Scholar
  2. [2]
    Comstock, C., Singular perturbations of elliptic equations I,SIAM J. Appl. Math.,20 (1971), 491.MATHMathSciNetCrossRefGoogle Scholar
  3. [3]
    Ladyzhenskaya, O. A,The Boundary Problems of Mathematical Physics, Springer-Verlag (1985).Google Scholar

Copyright information

© Shanghai University of Technology (SUT) 1991

Authors and Affiliations

  • Su Yu-cheng
    • 1
  • Liu Guo-qing
    • 2
  1. 1.Nanjing UniversityNanjing
  2. 2.Nanjing Institute of Chemical TechnologyNanjing

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