Abstract: A finite difference method with accuracies of fourth order in space and second order in time is proposed for time-periodic solutions of a nonlinear parabolic boundary value problem. A monotone iterative scheme is developed for proving the existence and uniqueness of the periodic solutions of the nonlinear discrete scheme, and the computational algorithms for the periodic solutions are also provided. The convergence of the discrete scheme is discussed. The numerical results show the advantages of the method.

Key words: time-periodic solution, finite difference scheme, monotone iteration, high accuracy, nonlinear parabolic boundary value problem, time-periodic solution, finite difference scheme, monotone iteration, high accuracy