华东师范大学学报(自然科学版) ›› 2006, Vol. 2006 ›› Issue (1): 72-79.

• 数学 统计学 • 上一篇    下一篇

非线性抛物型方程时间周期解的有限差分方法(英)

魏 玮, 王元明   

  1. 华东师范大学 数学系, 上海 200062
  • 收稿日期:2004-07-06 修回日期:2004-12-07 出版日期:2006-01-25 发布日期:2006-01-25
  • 通讯作者: 王元明

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

WEI Wei, WANG Yuan-ming   

  1. Department of Mathematics, East China Normal University, Shanghai 200062, China
  • Received:2004-07-06 Revised:2004-12-07 Online:2006-01-25 Published:2006-01-25
  • Contact: WANG Yuan-ming

摘要： 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.

关键词: 非线性抛物型方程, 周期解 有限差分方法 高精度 单调迭代, 非线性抛物型方程, 周期解 有限差分方法 高精度 单调迭代

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

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