Numerical Method for the System of Reaction-Diffusion Equations with a Small Parameter

Pan Zhong-xiong; Wang Yi-fei

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 1991 > 12(8): 761-767

Pan Zhong-xiong, Wang Yi-fei. Numerical Method for the System of Reaction-Diffusion Equations with a Small Parameter[J]. Applied Mathematics and Mechanics, 1991, 12(8): 761-767.

Citation:

Pan Zhong-xiong, Wang Yi-fei. Numerical Method for the System of Reaction-Diffusion Equations with a Small Parameter[J]. Applied Mathematics and Mechanics, 1991, 12(8): 761-767.

Citation:

Pan Zhong-xiong, Wang Yi-fei. Numerical Method for the System of Reaction-Diffusion Equations with a Small Parameter[J]. Applied Mathematics and Mechanics, 1991, 12(8): 761-767.

PDF( 400 KB)

Numerical Method for the System of Reaction-Diffusion Equations with a Small Parameter

Shanghai University of Science and Technology, Shanghai

Received Date: 1989-11-15
Publish Date: 1991-08-15

Abstract

Abstract

This paper deals with the numerical method for the system of reaction-diffusion equations with a small parameter. It is difficult to solve the problems of this kind numerically because of the boundary layer efect Besed on singular perturbed theory and Greens function, we have established the difference scheme that is suited for the solution to the problems. We introduce an idea of feasitbe equidistant degree a here. And this proves that if a≥2 the scheme converges in norm with speed O(h+Δt) uniformly.
- boundary layer,
- Green’s function,
- feasible equidistant degree,
- uniform convergence

FullText(HTML)

References(7)

References

[1]	Nishiura,Y.,Stability analysis of travelling front solutions of reaction-diffusion systems an application of the step method,Proceedings of BAIL-IV(1986).
[2]	Nishiura,Y.,Layer stability analysis and those hold phenomenon of reaction-diffusion systems,SIAM J.Math.Anal.,13(1982).
[3]	Niijima,K.,A uniformly convergent difference scheme for a semilinear singular perturbation problem,Numer.Math.,43(1984).
[4]	Lorenz,J.,Non-linear boundary value problems with turning points and properties of difference schemes,Lecture Notes in Mathematics,New York,942(1982).
[5]	徐至展、潘仲雄、王翼飞、张文琦.激光核聚变的一维三温度计算,物理学报,31(9)(1982).
[6]	Smeller,J.,Shock Waves and Reaction-Diffusion Equations,Springer-Verlag(1980).
[7]	Pan Zhong-xiong and Wang Yi-fei,Numerical method for an evolutive system of nonlinear equations with a small parameter,Proceedings of BAIL-V(1988).