| 求解非线性刚性初值问题的隐显线性多步方法的误差分析 |
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| 引用本文： | 张根根,易星,肖爱国.求解非线性刚性初值问题的隐显线性多步方法的误差分析[J].计算数学,2015,37(1):1-13. |
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| 作者姓名： | 张根根 易星 肖爱国 |
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| 作者单位： | 湘潭大学数学与计算科学学院, 湖南湘潭 411105 |
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| 基金项目： | 国家自然科学基金项目(No.11271311),教育部创新团队项目(No.IRT1179)及湖南省教育厅重点项目(No.14A146). |
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| 摘 要： | 隐显线性多步方法由隐式线性多步方法和显式线性多步法组合而成.本文主要讨论求解满足单边Lipschitz条件的非线性刚性初值问题和一类奇异摄动初值问题的隐显线性多步方法的误差分析.最后,由数值例子验证了所获的理论结果的正确性及方法处理这两类问题的有效性.
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| 关 键 词： | 刚性问题 奇异摄动问题 隐显多步方法 误差分析 |
| 收稿时间： | 2013-12-28; |
ERROR ANALYSIS OF THE IMPLICIT-EXPLICIT LINEAR MULTISTEP METHODS FOR THE NONLINEAR STIFF INITIAL-VALUE PROBLEMS |
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| Zhang Gengen,Yi Xing,Xiao Aiguo.ERROR ANALYSIS OF THE IMPLICIT-EXPLICIT LINEAR MULTISTEP METHODS FOR THE NONLINEAR STIFF INITIAL-VALUE PROBLEMS[J].Mathematica Numerica Sinica,2015,37(1):1-13. |
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| Authors: | Zhang Gengen Yi Xing Xiao Aiguo |
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| Institution: | School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, Hunan, China |
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| Abstract: | Implicit-explicit linear multistep methods are composed of implicit linear multistep methods and explicit linear multistep methods. In this paper, we are focused on error analysis of the implicit-explicit linear multistep methods for the nonlinear stiff initial-value problems satisfying the one-sided Lipschitz condition and a class of singularly perturbed initial-value problems. Numerical examples verify the validity of the obtained theoretical results and the effectiveness of the implicit-explicit linear multistep methods. |
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| Keywords: | Stiff problems Singular perturbation problems Implicit-explicit linear multistep methods Error analysis |
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