一类时滞非线性抛物型方程的数值解法

Numerical Method for Nonlinear Parabolic Equations with Time Delay

利用上下解方法及相应的单调迭代方法,建立一个用于求解一类时滞非线性抛物型方程时间周期解的有限差分格式,在空间和时间方向上该格式分别具有四阶和二阶精度,并证明了周期解的存在惟一性,给出了一个求解算法,同时讨论了数值解的收敛性.数值结果表明了所给方法的优越性.

By means of the method of upper and lower solutions and its associated monotone iteration, a finite difference method with an accuracy of order four in space and an accuracy of order two in time is proposed for time-periodic solutions of a nonlinear parabolic equation with time delay. The existence and unique of periodic solutions were verified. The computational algorithms were provided for the periodic solutions, and the convergence of the discrete scheme was discussed. The numerical results demonstrate the advantages of the method.