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求解非线性时滞双曲型偏微分方程的紧致差分方法及Richardson外推算法

张启峰1, 张诚坚1, 邓定文2   

  1. 1. 华中科技大学数学与统计学院, 武汉 430074;
    2. 南昌航空大学数学与信息科学学院, 南昌 330063
  • 收稿日期:2012-05-28 出版日期:2013-09-15 发布日期:2013-09-06
  • 通讯作者: 张诚坚(E-Mail: cjzhang@mail.hust.edu.cn).
  • 基金资助:

    国家自然科学基金资助项目(11171125);国家自然科学基金重大研究计划重点项目(9113000);湖北省自然科学基金资助项目(2011CDB289)和国家留学基金项目(201306160037).

张启峰, 张诚坚, 邓定文. 求解非线性时滞双曲型偏微分方程的紧致差分方法及Richardson外推算法[J]. 数值计算与计算机应用, 2013, 34(3): 167-176.

Zhang Qifeng, Zhang Chengjian, Deng Dingwen. A COMPACT DIFFERENCE SCHEME AND RICHARDSON EXTRAPOLATION ALGORITHM FOR SOLVING A CLASS OF THE NONLINEAR DELAY HYPERBOLIC PARTIAL DIFFERENTIAL EQUATIONS[J]. Journal of Numerical Methods and Computer Applications, 2013, 34(3): 167-176.

A COMPACT DIFFERENCE SCHEME AND RICHARDSON EXTRAPOLATION ALGORITHM FOR SOLVING A CLASS OF THE NONLINEAR DELAY HYPERBOLIC PARTIAL DIFFERENTIAL EQUATIONS

Zhang Qifeng1, Zhang Chengjian1, Deng Dingwen2   

  1. 1. Huazhong University of Science and Technology, School of Mathematics and Statistics, Wuhan 430074, China;
    2. College of Mathematics and Information Science, Nanchang Hangkong University, Nanchang 330063, China
  • Received:2012-05-28 Online:2013-09-15 Published:2013-09-06
本文构造了一类求解非线性时滞双曲型偏微分方程的紧致差分格式, 获得了该差分格式的唯一可解性, 收敛性和无条件稳定性, 收敛阶为O(τ2+h4), 并进一步对时间方向进行Richardson外推, 使得收敛阶达到O(τ4+h4). 数值实验表明了算法的精度和有效性.
In this paper, a class of compact difference schemes are constructed to solve the nonlinear delay hyperbolic partial differential equations. The unique solvability, convergence and unconditional stability of the scheme are obtained. The convergence order is O(τ2+h4). Furthermore, the Richardson extrapolation is applied to improve the temporal accuracy of the scheme, and a solution of order four in both temporal and spatial dimensions is obtained. Numerical example shows the accuracy and efficiency of the algorithms.

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