Discontinuous solutions of neutral delay differential equations |
| |
| Institution: | 1. Mathematics Department, University College Chester, Chester CH1 4BJ, UK;2. School of Mathematics, University of Manchester, Manchester M13 9PL, UK;1. Dipartimento di Matematica e Informatica “U. Dini”, Università di Firenze, Italy;2. Dipartimento di Matematica, Università di Bari, Italy;1. Department of Mathematics, Technische Universität Darmstadt, Dolivostraße 15, 64293 Darmstadt, Germany;2. Graduate School of Computational Engineering, TU Darmstadt, Germany;3. Department of Mathematics, Martin-Luther Universität Halle–Wittenberg, Postbox D-06099 Halle (Saale), Germany;1. School of Sciences, Hangzhou Dianzi University, Hangzhou, Zhejiang 310018, China;2. Department of Mathematical Sciences, University of Nevada Las Vegas, Las Vegas, NV 89154, USA;1. School of Mathematics, Hunan University, Changsha 410082, China;2. Hunan Provincial Key Laboratory of Intelligent Information Processing and Applied Mathematics, Changsha 410082, China |
| |
| Abstract: | It is well known that the solutions of delay differential and implicit and explicit neutral delay differential equations (NDDEs) may have discontinuous derivatives, but it has not been appreciated (sufficiently) that the solutions of NDDEs—and, therefore, solutions of delay differential algebraic equations—need not be continuous. Numerical codes for solving differential equations, with or without retarded arguments, are generally based on the assumption that a solution is continuous. We illustrate and explain how the discontinuities arise, and present some methods to deal with these problems computationally. The investigation of a simple example is followed by a discussion of more general NDDEs and further mathematical detail. |
| |
| Keywords: | |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
