]*>","")" /> 修正局部Crank-Nicolson法对于二维热传导方程的应用

• 论文 •

### 修正局部Crank-Nicolson法对于二维热传导方程的应用

1. 新疆大学数学系
• 出版日期:1997-03-14 发布日期:1997-03-14

### A CORRECTOR LOCAL C-N METHOD FOR THE TWO-DIMENSIONAL HEAT EQUATION

1. Abdirishit Abduwali(Department of Mathematics, Xinjiang University)
• Online:1997-03-14 Published:1997-03-14
This paper describes a numerical method for solving initial-boundary value problems of parabolic equations. Based on a representation of the Trotter product,we derive a new technigue for two-dimensional problems, which does not yield a large linear system, by using a splitting of the coefficient matrix. Furthermore,we prove that the proposed method, which is explicit, and unconditionally stable.Some numerical examples show that our method is superior to the Crank-Nicolson method.
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 [1] N.N. Yanenko, The Method of Fractional Steps, Springer-Verlag, l971. [2] P.G. Ciarlet and Lions J.L. Editors,. Handbook of Numerical Analysis, North-HOlland, 1(1990). [3] A. Abdirishit, M. Sakakihara and H. Niki, A local Crank-Nicolson method for solving theheat equation, Hroshima Mathematical Journal, 23: 3 (1993). [4]阿不都热西提,仁木,二次元热方程式:对局所 Crank-Nicolson 法,日本应用数学理学会论文 集,2:4(1992);267-283. [5]阿不都热西提,仁木,方程式对局所Crank-Nicolson法,日本京都大学 数理解析研究所究录 787,短期共同研究, 6(1992), 176—187. [6]阿不都热西提·阿不都外力,修正局部C-N法对于一线热传导方程的定式化,待发表. [7] J. Weidmann, Linear Operators in Hilbert Space, Springer-Verlag, 1980.
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