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 feasilbe equidistant degree a here. And this proves that if a⩾2. the scheme converges in l1(m) norm with speed O(h+Δt) uniformly.
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References
Nishiura, Y., Stability analysis of travelling front solutions of reaction-diffusion systems — an application of the step method,Proceedings of BAIL-IV (1986).
Nishiura, Y., Layer stability analysis and those hold phenomenon of reaction-diffusion systems,SIAM J. Math. Anal.,13 (1982).
Niijima, K., A uniformly convergent difference scheme for a semilinear singular perturbation problem,Numer. Math.,43 (1984).
Lorenz, J., Non-linear boundary value problems with turning points and properties of difference schemes,Lecture Notes in Mathematics, New York, 942 (1982).
Xu Zhi-zhan, Pan Zhong-xiong, Wang Yi-fei and Zhang Wen-qi, One-dimensional three-temperature calculations for laser fusion,Acta Physica Sinica,31, 9 (1982). (in Chinese)
Smeller, J.,Shock Waves and Reaction-Diffusion Equations, Springer-Verlag (1980).
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).
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Communicated by Jiang Fu-ru
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Zhong-xiong, P., Yi-fei, W. Numerical method for the system of reaction-diffusion equations with a small parameter. Appl Math Mech 12, 813–819 (1991). https://doi.org/10.1007/BF02458172
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DOI: https://doi.org/10.1007/BF02458172