On the Convergence of the Matrix Lambert W Approach to Solution of Systems of Delay Differential Equations
| Autor: | A. Galip Ulsoy, Rita Gitik |
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| Rok vydání: | 2018 |
| Předmět: |
0209 industrial biotechnology
bepress|Engineering Mechanical Engineering 020208 electrical & electronic engineering bepress|Engineering|Mechanical Engineering engrXiv|Engineering|Mechanical Engineering 02 engineering and technology Delay differential equation Computer Science Applications symbols.namesake Matrix (mathematics) 020901 industrial engineering & automation engrXiv|Engineering Control and Systems Engineering Lambert W function Convergence (routing) 0202 electrical engineering electronic engineering information engineering symbols Applied mathematics bepress|Engineering|Mechanical Engineering|Acoustics Dynamics and Controls engrXiv|Engineering|Mechanical Engineering|Acoustics Dynamics and Controls Instrumentation Information Systems Mathematics |
| DOI: | 10.31224/osf.io/rfmd5 |
| Popis: | Convergence of the matrix Lambert W function method for solving systems of delay differential equations (DDEs) is considered. Recent research shows that convergence problems occur with certain DDEs when using the well-established Q-iteration approach. A complementary, and recently proposed, W-iteration approach is shown to converge even on systems where Q-iteration fails. Furthermore, the role played by the branch numbers k = −∞ … −1, 0, 1, … ∞ of the matrix Lambert W function, Wk, in terms of initializing the iterative solutions, is also discussed and elucidated. Several second-order examples, known to have convergence problems with Q-iteration, are readily solved by W-iteration. Examples of third- and fourth-order DDEs show that W-iteration is also effective on higher-order systems. |
| Databáze: | OpenAIRE |
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