| 波动方程辛算法的迭代求解 |
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| 引用本文： | 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. |
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| 作者姓名： | 蒋长锦 |
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| 作者单位： | 中国科学技术大学数学系, 安徽 合肥 230026 |
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| 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+Δt2l)和O(Δx4+Δt2l)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.
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| 关 键 词： | Hamilton系统 辛差分格式 迭代解法 收敛条件 |
| 文章编号： | 1001-246X(2002)01-0013-04 |
| 收稿时间： | 2000-09-18 |
| 修稿时间： | 2000年9月18日 |
ITERATIVE METHODS FOR SYMPLECTIC ALGORITHM OF WAVE EQUATION |
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| 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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| Authors: | JIANG Chang-jin |
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| Institution: | Department of Mathematics, University of Science and Technology of China, Hefei 230026, P R China |
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| 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+ Δt2l) and O(Δx4+ Δt2l), 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. |
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| Keywords: | Hamiltonian systems symplectic difference schemes iterative methods conditions of convergence |
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