| 刚性积分微分方程的几类高效隐式并行方法 |
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| 引用本文： | 刘红良,李利娟,李寿佛.刚性积分微分方程的几类高效隐式并行方法[J].湘潭大学自然科学学报,2006,28(1):12-16,45. |
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| 作者姓名： | 刘红良 李利娟 李寿佛 |
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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： | 国家科技攻关项目;中国科学院资助项目 |
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| 摘 要： | 为求解刚性积分微分方程提供几类高效隐式并行方法,通过数值实验,进一步证实了李寿佛建立的刚性Volterra泛函微分方程数值方法B-理论有关猜想的正确性,同时通过对并行多值混合方法和Lobatto IIIC方法的数值结果进行分析和比较,发现李寿佛所创立的并行多值混合方法比Bellen极力推荐的Lobatto IIIC方法更具优势.
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| 关 键 词： | 刚性积分微分方程 泛函微分方程 高效并行方法 B-理论 |
| 文章编号： | 1000-5900（2006）01-0012-05 |
| 收稿时间： | 2005-04-30 |
| 修稿时间： | 2005-04-30 |
Several Classes of Efficient Numerical Implicit Parallel Methods for Solving Stiff Integro-Differential Equations |
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| LIU Hong-liang,LI Li-juan,LI Shou-fu.Several Classes of Efficient Numerical Implicit Parallel Methods for Solving Stiff Integro-Differential Equations[J].Natural Science Journal of Xiangtan University,2006,28(1):12-16,45. |
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| Authors: | LIU Hong-liang LI Li-juan LI Shou-fu |
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| Institution: | School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105 China |
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| Abstract: | Several classes of efficient numerical implicit parallel methods are recommended for solving stiff integro-differential equations,and the validity of B-theory of numerical methods for Volterra functional differential equations(VFDEs) presented by Li Shoufu in 2001 is further demonstrated by a series of numerical experiments using the methods recommended above.Furthermore,the characteristic and the advantages of parallel multivalue hybrid methods(PMHMs) and Lobatto IIIC methods are illuminated,respectively,by analysing and comparing the numerical results,the PMHM methods created by Li Shoufu is superior to the Lobatto IIIC methods. |
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| Keywords: | Stiff integro-differential equations Volterra functional differential equations Efficient numerical parallel methods B-theory |
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