波动方程辛算法的迭代求解

计算物理 ›› 2002, Vol. 19 ›› Issue (1): 13-16.

波动方程辛算法的迭代求解

蒋长锦

中国科学技术大学数学系, 安徽合肥 230026

收稿日期:2000-09-18 修回日期:2001-01-09 出版日期:2002-01-25 发布日期:2002-01-25
作者简介:蒋长锦(1943-),男,安徽,副教授,从事计算数学、计算物理方面的研究.

ITERATIVE METHODS FOR SYMPLECTIC ALGORITHM OF WAVE EQUATION

JIANG Chang-jin

Department of Mathematics, University of Science and Technology of China, Hefei 230026, P R China

Received:2000-09-18 Revised:2001-01-09 Online:2002-01-25 Published:2002-01-25

摘要/Abstract

摘要： 对(∂²)/(∂x²)利用中心差商算子,对expt作对角Padé逼近,由波动偏微分方程可得到两类具有O(Δx²+Δt^2l)和O(Δx⁴+Δt^2l)精度的辛格式.对由此类辛格式产生的线性方程组构造了两种迭代解法,并对l=1,2,3,4给出了它们的收敛条件.并进行了数值实验.

关键词: Hamilton系统, 辛差分格式, 迭代解法, 收敛条件

Abstract: By using the central difference quotient operator for (∂²)/(∂x²) and the diagonal Padé approximation of exp t, two kinds of symplectic schemes which have accuracy O(Δx²+ Δt^2l) and O(Δx⁴+ Δt^2l), respectively, can be attained for wave partial differential equation. Two iterative methods are described for the linear systems formed from the above schemes. Their conditions of convergence are given for l=1,2,3,4. The numerical experiments demonstrate that the symplectic algorithm have efficiency and both methods are convergent.

Key words: Hamiltonian systems, symplectic difference schemes, iterative methods, conditions of convergence

中图分类号:

O241

蒋长锦. 波动方程辛算法的迭代求解[J]. 计算物理, 2002, 19(1): 13-16.

JIANG Chang-jin. ITERATIVE METHODS FOR SYMPLECTIC ALGORITHM OF WAVE EQUATION[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2002, 19(1): 13-16.

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