van Horssen, W. T. On asymptotic approximations of first integrals for differential and difference equations. (English) Zbl 1141.39017 J. Indones. Math. Soc. 13, No. 1, 1-15 (2007). 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. Reviewer: Zhiming Guo (Guangzhou) Cited in 1 ReviewCited in 2 Documents MSC: 39A11 Stability of difference equations (MSC2000) 34A05 Explicit solutions, first integrals of ordinary differential equations Keywords:perturbation method; integrating factor; invariance factor; ordinary differential equation; ordinary difference equation; first integral; functional equation PDFBibTeX XMLCite \textit{W. T. van Horssen}, J. Indones. Math. Soc. 13, No. 1, 1--15 (2007; Zbl 1141.39017) Full Text: EuDML