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Nonlinear Stability of General Linear Methods for Delay Differential Equations |
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| Authors: | Chengming Huang Shoufu Li Hongyuan Fu Guangnan Chen |
| Affiliation: | (1) Department of Mathematics, Huazhong University of Science and Technology, Wuhan, 430074, P.R. China;(2) Department of Mathematics, Xiangtan University, Hunan Province, 411105, P.R.China;(3) Graduate school, CAEP, P.O. Box 2101, Beijing, 100088, P.R.China |
| Abstract: | This paper is devoted to a study of nonlinear stability of general linear methods for the numerical solution of delay differential equations in Hilbert spaces. New stability concepts are further introduced. The stability properties of (k,p,q)-algebraically stable general linear methods with piecewise constant or linear interpolation procedure are investigated. We also discuss stability of linear multistep methods viewed as a special subset of the class of general linear methods. |
| Keywords: | Delay differential equations general linear methods nonlinear stability |
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