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On asymptotic approximations of first integrals for differential and difference equations. (English) Zbl 1141.39017

The concept of integrating factors for differential equations and the concept of invariance factors for difference equations to obtain first integral or invariants are presented. It is shown that all integral factors have to satisfy a system of partial differential equation, and that all invariance factors have to satisfy a functional equation. The author reviewed the perturbation method based on the integrating factors, which was developed to approximate first integrals for systems of ordinary differential equations. Also a first result in the development of the perturbation method for difference equation based on invariance factors is presented.

MSC:

39A11 Stability of difference equations (MSC2000)
34A05 Explicit solutions, first integrals of ordinary differential equations
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