Abstract:

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.

Key words: nonlinear parabolic equation, time delay, timeperiodic solution, finite difference scheme, high accuracy, monotone iteration