| 积分微分方程线性多步方法的散逸性 |
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| 引用本文： | 蔡白光,甘四清.积分微分方程线性多步方法的散逸性[J].纯粹数学与应用数学,2011,27(5):603-608. |
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| 作者姓名： | 蔡白光 甘四清 |
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| 作者单位： | 1. 海南大学信息科学技术学院,海南海口,570228
2. 中南大学数学与计算科学学院,湖南长沙,410075 |
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| 基金项目： | 国家自然科学基金，海南省自然科学基金，海南大学青年基金 |
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| 摘 要： | 研究一类积分微分方程线性多步方法（p，σ）的散逸性．当积分项用复合求积公式逼近时，证明了线性多步方法是有限维散逸的．这说明该方法很好地继承了系统本身所具有的重要性质．这一结论为数值求解这一类微分方程提供了更多的选择．
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| 关 键 词： | 积分微分方程 散逸性 线性多步方法 复合求积公式 |
Dissipativity of linear multistep metheds for integro-differential equations |
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| CAI Bai-guang ,GAN Si-qing.Dissipativity of linear multistep metheds for integro-differential equations[J].Pure and Applied Mathematics,2011,27(5):603-608. |
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| Authors: | CAI Bai-guang GAN Si-qing |
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| Institution: | CAI Bai-guang 1,GAN Si-qing 2(1.Department of Mathematics,College of Information Science and Technology,Hainan University,Haikou 570228,China,2.School of Mathematics Science and Computing Technology,Central South University,Changsha 410075,China) |
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| Abstract: | This paper is concerned with the dissipativity of linear multistep methods（p, σ） for one kind of integro-differential equations. When the integration term is approximated by the compound quadrature formula, we prove that the linear multistep methods are dissipative in finite-dimentional space. It is shown that the linear multistep methods can inherit the important property of the underlying systems. The result make me have more choice to solve the underlying systems. |
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| Keywords: | integro-differential equation dissipativity linear multistep methods compound quadrature formula |
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