An analytic-numerical method of computation of the Liapunov and period constants derived from their algebraic structure
We consider the problem of computing the Liapunov and the period constants for a smooth differential equation with a non degenerate critical point. First, we investigate the structure of both constants when they are regarded as polynomials on the coefficients of the differential equation. Secondly,...
| Autores: | , , |
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| Formato: | artículo |
| Fecha de publicación: | 1996 |
| País: | España |
| Recursos: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/947 |
| Acesso em linha: | https://hdl.handle.net/2117/947 |
| Access Level: | acceso abierto |
| Palavra-chave: | Ordinary Differential Equations and Operators, Symposium on Differential equations centre point Liapunov constants isochronicity analytic-numerical method Equacions diferencials ordinàries Classificació AMS::34 Ordinary differential equations::34C Qualitative theory Classificació AMS::34 Ordinary differential equations::34D Stability theory Classificació AMS::65 Numerical analysis::65L Ordinary differential equations |
| Resumo: | We consider the problem of computing the Liapunov and the period constants for a smooth differential equation with a non degenerate critical point. First, we investigate the structure of both constants when they are regarded as polynomials on the coefficients of the differential equation. Secondly, we take advantadge of this structure to derive a method to obtain the explicit expression of the above-mentioned constants. Although this method is based on the use of the Runge-Kutta-Fehlberg methods of orders 7 and 8 and the use of Richardson's extrapolation, it provides the real expression for these constants. |
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