Numerical Solutions for Singularly Perturbed Semi-linear Parabolic Equation

Wu Qi-guang; Li Ji-chun

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 1993 > 14(9): 753-761

Wu Qi-guang, Li Ji-chun. Numerical Solutions for Singularly Perturbed Semi-linear Parabolic Equation[J]. Applied Mathematics and Mechanics, 1993, 14(9): 753-761.

Citation:

Wu Qi-guang, Li Ji-chun. Numerical Solutions for Singularly Perturbed Semi-linear Parabolic Equation[J]. Applied Mathematics and Mechanics, 1993, 14(9): 753-761.

Citation:

Wu Qi-guang, Li Ji-chun. Numerical Solutions for Singularly Perturbed Semi-linear Parabolic Equation[J]. Applied Mathematics and Mechanics, 1993, 14(9): 753-761.

PDF( 475 KB)

Numerical Solutions for Singularly Perturbed Semi-linear Parabolic Equation

Depi. of Math., Nanjing Univ., Nanjing

Received Date: 1992-04-30
Publish Date: 1993-09-15

Abstract

Abstract

In this paper, we discuss singularly perturbed semi-linear parabolic equations for one dimension and two dimension, we find numerical solutions by using both the line-method and the exact difference scheme on a special non-uniform discretization mesh. The uniform convergence in ε of the first order accuracy is obtained.
- uniform convergence,
- parabolic equations,
- non-uniform mesh

FullText(HTML)

References(4)

References

[1]	Trenogin,V.A.,Asymtotic solution of linear parabolic equation with parabolic boundary layer,Uspehi Mat.Nauk,16(1)(97),(1961),163-169.
[2]	Boglaev.I.P.,Numerical solution of nonlinear boundary value problem with a small parameter in the highest derivate,U.S.S.R.Comp.Math.Phys.,24(1984),1649-1956.
[3]	Dooaln,R.P.,J.J.H.Miller and W.H.A.Schilders.Uniform Numerical Methods for Problems with Initial and Boundary Layers,Boole Press,Dublin,1980.
[4]	Oleinik,O.A.and E.V.Radkevic,Second order equations with nonnegative characteristic form,American Mathematical Society,Rhode Island and Plenum Press,New York,(1973).