马明书, 马小霞, 任祯琴, 马文娟. 二维变系数反应扩散方程的紧交替方向差分格式[J]. 信阳师范学院学报(自然科学版), 2009, 22(1): 21-24.
引用本文: 马明书, 马小霞, 任祯琴, 马文娟. 二维变系数反应扩散方程的紧交替方向差分格式[J]. 信阳师范学院学报(自然科学版), 2009, 22(1): 21-24.
MA Ming-shu, MA Xiao-xia, REN Zhen-qin, MA Wen-juan. A Compact Alternate Direct Implicit Difference Method for the Reaction Diffusion Equations of Two-Di[J]. Journal of Xinyang Normal University (Natural Science Edition), 2009, 22(1): 21-24.
Citation: MA Ming-shu, MA Xiao-xia, REN Zhen-qin, MA Wen-juan. A Compact Alternate Direct Implicit Difference Method for the Reaction Diffusion Equations of Two-Di[J]. Journal of Xinyang Normal University (Natural Science Edition), 2009, 22(1): 21-24.

二维变系数反应扩散方程的紧交替方向差分格式

A Compact Alternate Direct Implicit Difference Method for the Reaction Diffusion Equations of Two-Di

  • 摘要: 研究二维抛物型方程的紧交替方向隐式差分格式.首先综合运用算子方法导出紧差分格式,并给出了差分格式截断误差的表达式;其次引进过渡层变量,给出了紧交替方向隐式差分格式算法;接着利用Fourier稳定性分析方法证明了差分格式的稳定性和收敛性,且收敛阶为O(2τ+h4);最后给出了数值例子,数值结果和理论结果是吻合的.

     

    Abstract: This paper presents a compact alternate direct implicit difference scheme of high accuracy for solving the two-dimensional constant coefficient reaction-diffusion equations.Firstly,a compact difference scheme is derived by using operator method and an error estimate of O(τ2+h4)is given in detail.Secondly,a compact ADI difference scheme is presented by introducing a variable of intermediate value.Thirdly,the stability and convergence of the ADI scheme are achieved by using Fourier method.Finally,a numercial ...

     

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