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Stability Analysis of Runge-Kutta Methods for Non-Linear Delay Differential Equations
Authors:Huang Chengming  Fu Hongyuan  Li Shoufu  Chen Guangnan
Institution:(1) Department of Mathematics, Xiangtan University, Hunan Province, 411105, P.R. China;(2) Graduate School, CAEP, P.O. Box 2101, Beijing, 100088, P.R. China
Abstract:This paper is concerned with the numerical solution of delay differential equations(DDEs). We focus on the stability behaviour of Runge-Kutta methods for nonlinear DDEs. The new concepts of GR(l)-stability, GAR(l)-stability and weak GAR(l)-stability are further introduced. We investigate these stability properties for (k, l)-algebraically stable Runge-Kutta methods with a piecewise constant or linear interpolation procedure.
Keywords:Delay differential equations  Runge-Kutta methods  nonlinear stability
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