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

Volume 13 Issue 4

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Article Navigation > Applied Mathematics and Mechanics > 1992 > 13(4): 279-286

Su Yu-cheng, Zhang You-yu. Difference Scheme for an Initial-Boundary Value Problem for Linear Coefficient-Varied Parabolic Differential Equation with a Nonsmooth Boundary Layer Function[J]. Applied Mathematics and Mechanics, 1992, 13(4): 279-286.

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Difference Scheme for an Initial-Boundary Value Problem for Linear Coefficient-Varied Parabolic Differential Equation with a Nonsmooth Boundary Layer Function

Nanjing University, Nanjing

Received Date: 1990-12-25
Publish Date: 1992-04-15

Abstract

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 εis given, and error estimate and numerical result are also given.
- nonsmooth boundary layer,
- characteristic boundary,
- nonuniform mesh,
- exponentially fitted,
- uniformly convergent difference scheme,
- parabolic differential equation

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References(6)

References

[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.
[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.
[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.
[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).
[5]	Richards,Verga.,Matrix Iterative Analysis,Prentice Hall,Englewood Cliffs,N.J.(1962).
[6]	Friedman,A.,Partial Differential Equations of Parabolic Type,Prentice-Hall,Inc.(1964).

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