非线性抛物型方程时间周期解的有限差分方法(英文)

A Finite Difference Method for Time-periodic Solutions of Nonlinear Parabolic Equations

建立了一个用于求解非线性抛物型方程时间周期解的有限差分方法,在空间和时间方向上该方法分别具有四阶和两阶精度．为了证明解的存在唯一性,建立了一个单调迭代算法,该算法也给出了一个求解算法．同时讨论了数值解的收敛性．数值结果显示了该方法的优越性．

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.