| 刚性常微分方程组初值问题的多重网格解法 |
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| 引用本文： | 蒋长锦.刚性常微分方程组初值问题的多重网格解法[J].中国科学技术大学学报,1991,21(1):78-86. |
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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 |
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| 摘 要： | 描述了求解刚性常微分方程组初值问题的多重网格方法。具体选择了光滑算子构造了有关的多重网格分量,阐明了方法的收敛性。它不仅具有隐式Runge-Kutta方法的优点,而且可以不必求解由隐式方法产生的非线性方程组。给出的计算实例显示了快速收敛性。
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| 关 键 词： | 刚性常微分方程组 多重网格方法 光滑算子 粗网格校正 |
A Multigrid Method for Solving Stiff Systems of Numerical Initial Value Problems in Ordinary Differential Equations |
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| Jiang Changjin.A Multigrid Method for Solving Stiff Systems of Numerical Initial Value Problems in Ordinary Differential Equations[J].Journal of University of Science and Technology of China,1991,21(1):78-86. |
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| Authors: | Jiang Changjin |
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| Institution: | Department of Mathematics |
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| Abstract: | In this paper, a multigrid method for solving stiff systems of numerical initial value problems in ordinary differential equations is devoloped. The multigrid components are struetuered, and the convergenee properties of this method interpreted. This method not only has the advantage of implicit Runge- Kutta methods but does not need to solve the nonlinear systems of implicit Runge- Kutta methods. AS a numerical example, a method for solving nonliner papabolic differential equation is described, and the numerical result shows the rapid speed of convergence. |
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