Applied Mathematics and Mechanics

, Volume 13, Issue 4, pp 297–304 | Cite as

Difference scheme for an initial-boundary value problem for linear coefficient-varied parabolic differential equation with a nonsmooth boundary layer function

  • Su Yu-cheng
  • Zhang You-yu
Article
  • 17 Downloads

Abstract

In this paper, using nonuniform mesh and exponentially fitted difference method, a uniformly convergent difference scheme for an initial-boundary value problem of linear parabolic differential equation with the nonsmooth boundary layer function with respect to small parameter ε is given, and error estimate and numerical result are also given.

Key words

nonsmooth boundary layer characteristic boundary nonuniform mesh exponentially fitted uniformly convergent difference scheme parabolic differential equation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Butuzov, V.F. and A.V. Nesterov, On the asymptotics of the solution of an equation of parabolic type with small parameters affecting the highest derivatives,J. Vycisl. Mathem. and Mathem. Phys.,22, 4 (1982), 865–870.MATHMathSciNetGoogle Scholar
  2. [2]
    Shishkin, G.I., Numerical solution of the boundary value problem for elliptic equations with small parameter at the leading derivative,USSR Computational Math. Math. Phys.,26, 7–8 (1986), 1019–1031.MATHMathSciNetGoogle Scholar
  3. [3]
    Bakhvalov, N.S., The optimization of methods of solving boundary value problems with a boundary layer,USSR Computational Math. Math. Phys.,9, 4 (1969) 841–859.MATHGoogle Scholar
  4. [4]
    Doolan, E.P., J.J.H. Miller and W.H.A. Schilders,Uniform Numerical Methods for Problems with Initial and Boundary Layers, Boole Press, Dublin (1980).Google Scholar
  5. [5]
    Richards, Verga.,Matrix Iterative Analysis, Prentice Hall, Englewood Cliffs, N.J. (1962).Google Scholar
  6. [6]
    Friedman, A.,Partial Differential Equations of Parabolic Type, Prentice-Hall, Inc. (1964).Google Scholar

Copyright information

© Shanghai University of Technology (SUT) 1992

Authors and Affiliations

  • Su Yu-cheng
    • 1
  • Zhang You-yu
    • 1
  1. 1.Nanjing UniversityNanjing

Personalised recommendations