A geometric treatment of reduction of order of ordinary difference equations
| Autor: | G B Byrnes |
|---|---|
| Rok vydání: | 1995 |
| Předmět: |
Differential equation
Independent equation Mathematical analysis General Physics and Astronomy Reduction of order Statistical and Nonlinear Physics Euler equations Stochastic partial differential equation symbols.namesake Collocation method symbols Differential algebraic equation Mathematical Physics Mathematics Separable partial differential equation |
| Zdroj: | Journal of Physics A: Mathematical and General. 28:4925-4944 |
| ISSN: | 1361-6447 0305-4470 |
| DOI: | 10.1088/0305-4470/28/17/023 |
| Popis: | We generalize the theory of Lie symmetries of ordinary difference equations to the nonautonomous case. A coordinate-invariant treatment in which solutions are sections of a fibre-bundle is employed. It is shown that Lie symmetries of difference equations must be projectable, which is not the case for differential equations. In fact this result extends to partial difference equations. We also show that a time-like symmetry can be used to reduce a nonautonomous difference equation to the autonomous case. Examples are given of this process and of the reduction of order of a nonautonomous system. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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