| 色散方程的交替分组迭代方法 |
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| 引用本文： | 刘洪华. 色散方程的交替分组迭代方法[J]. 山东大学学报(理学版), 2007, 42(1): 19-23 |
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| 作者姓名： | 刘洪华 |
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| 作者单位： | 山东大学,数学与系统科学学院,山东,济南,250100 |
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| 基金项目： | 国家自然科学基金;山东省自然科学基金 |
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| 摘 要： | 给出了求解具有周期边界条件色散方程近似解的交替分组迭代法.构造了逼近色散方程的两层隐式差分格式,以此隐式差分格式为基础设计出一种适合在并行机上进行计算的交替分组迭代方法,并证明了上述隐式差分格式的绝对稳定性和交替分组迭代过程的收敛性.数值试验对色散方程的隐格式与Crank-Nicolson格式分别应用交替分组迭代求解.结果表明,该方法具有很好的数值精度和良好的实用性.
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| 关 键 词： | 色散方程 交替分组迭代方法 绝对稳定 并行计算 |
| 文章编号： | 1671-9352（2007）01-0019-05 |
| 收稿时间： | 2006-04-27 |
| 修稿时间： | 2006-04-27 |
The alternating group iterative method for the dispersive equation |
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| LIU Hong-hua. The alternating group iterative method for the dispersive equation[J]. Journal of Shandong University, 2007, 42(1): 19-23 |
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| Authors: | LIU Hong-hua |
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| Affiliation: | School of Math. and System Sci., Shandong Univ. , Jinan 250100, Shandong, China |
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| Abstract: | The alternating group iterative method for the dispersive equation with periodic boundary condition is presented.A two-level implicit difference scheme is designed,and an alternating group iterative method is suggested which is capable of parallelism on parallel computer.In addition,unconditional stability of the difference scheme and convergence of the iterative process are proved.The alternating group iterative method is used to solve the implicit scheme and the Crank-Nicolson scheme of the disper-sive equation.The results show that this method has good accuracy and practicability. |
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| Keywords: | dispersive equation alternating group iterative method unconditionally stable parallel computation |
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