A Finite Difference Scheme for Nonlinear Reaction-diffusion Equations with Time Delay
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摘要: 建立了一个用于求解非线性时滞反应扩散方程的有限差分格式,在空间和时间方向上该格式分别具有四阶和两阶精度,用上下解方法给出了有限差分解的存在和唯一性,建立了一个单调迭代用于计算有限差分解,数值结果显示了该方法的优越性.Abstract: A finite difference scheme with the accuracy of fourth order in space and second order in time is proposed for solving a nonlinear reaction-diffusion equation with time delay. Existence and uniqueness of the solution is given by the method of upper and lower solutions. A monotone iteration is also developed for the computation of the finite difference solution. The convergence of the scheme is discussed. The numerical results shows the advantages of the method.
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