Formal solutions of differential equations. (English) Zbl 0727.12011
The author gives a survey of recent results in the theory of differential equations. The survey is made up from the viewpoint of differential algebra in general and connected with the first problem of Galois theory mainly. It includes methods for finding power series solutions, asymptotic methods etc. The methods of computer algebra systems such as MACSYMA are also discussed. The author poses some open questions and provides vast references.
Reviewer: N. V. Grigorenko (Kiev)
MSC:
| 12H05 | Differential algebra |
| 34A05 | Explicit solutions, first integrals of ordinary differential equations |
| 68W30 | Symbolic computation and algebraic computation |
| 34E05 | Asymptotic expansions of solutions to ordinary differential equations |
| 34-02 | Research exposition (monographs, survey articles) pertaining to ordinary differential equations |
| 12-02 | Research exposition (monographs, survey articles) pertaining to field theory |
Keywords:
survey; differential algebra; first problem of Galois theory; power series solutions; asymptotic methods; computer algebra systems; MACSYMAReferences:
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