Stability analysis of numerical methods for systems of functional-differential and functional equations

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• 作者：Huang ; Chengming ; Chang ; Qianshun
• 关键词：Hybrid systems ; Functional-differential equations ; Functional equations ; Linear multistep methods ; One-leg methods ; Runge-Kutta methods ; Numerical stability
• 刊名：Computers and Mathematics with Applications
• 出版年：2002
• 出版时间：September, 2002
• 年：2002
• 卷：44
• 期：5-6
• 页码：717-729
• 全文大小：648 K

文摘

This paper is concerned with the numerical solution of functional-differential and functional equations which include functional-differential equations of neutral type as special cases. The adaptation of linear multistep methods, one-leg methods, and Runge-Kutta methods is considered. The emphasis is on the linear stability of numerical methods. It is proved that A-stable methods can inherit the asymptotic stability of underlying linear systems. Some general results of stability on explicit and implicit methods are also given.