| Stability Analysis of Runge-Kutta Methods for Delay Integro-Differential Equations |
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| 作者姓名： | 甘四清 郑纬民 |
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| 作者单位： | DepartmentofComputerScienceandTechnology,TsinghuaUniversity,Beijing100084,China |
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| 基金项目： | Supported by the National Natural Science Foundation of China (Nos. 60273007，60131160743 and 10101027) and China Post-doctoral Science Foundation |
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| 摘 要： | Considering a linear system of delay integro-differential equations with a constant delay whose zero solution is asympototically stable, this paper discusses the stability of numerical methods for the system. The adaptation of Runge-Kutta methods with a Lagrange interpolation procedure was focused on inheriting the asymptotic stability of underlying linear systems. The results show that an A-stable Runge-Kutta method preserves the asympototic stability of underlying linear systems whenever an unconstrained grid is used.
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| 关 键 词： | 延迟积分微分方程 内插法 数值稳定性 Runge-Kutta方法 零解 |
Stability Analysis of Runge-Kutta Methods for Delay Integro-Differential Equations |
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| GAN Siqing,ZHENG Weimin.Stability Analysis of Runge-Kutta Methods for Delay Integro-Differential Equations[J].Tsinghua Science and Technology,2004,9(2):185-188. |
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| Authors: | GAN Siqing ZHENG Weimin |
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| Abstract: | Considering a linear system of delay integro-differential equations with a constant delay whose zero solution is asympototically stable, this paper discusses the stability of numerical methods for the sys-tem. The adaptation of Runge-Kutta methods with a Lagrange interpolation procedure was focused on in-heriting the asymptotic stability of underlying linear systems. The results show that an A-stable Runge-Kutta method preserves the asympototic stability of underlying linear systems whenever an unconstrained grid is used. |
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| Keywords: | delay integro-differential equations Runge-Kutta methods interpolation numerical stability |
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