带小参数的反应—扩散方程组的数值方法
Numerical Method for the System of Reaction-Diffusion Equations with a Small Parameter
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摘要: 本文讨论带小参数的反应—扩散方程组的数值方法.由于边界层效应,使得这类问题的数值求解十分困难.我们根据奇异摄动理论和Green函数方法建立起一种适合求解这类问题的差分格式.在文中,我们引入了可行等距度α,并证明了若a≥2则格式在l1(m)意义下一致收敛且收敛阶为O(h+△t).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.
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Key words:
- boundary layer /
- Green’s function /
- feasible equidistant degree /
- uniform convergence
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[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). -
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