Solving ordinary differential equations in terms of series with real exponents
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- by D. Yu. Grigor′ev and M. F. Singer PDF
- Trans. Amer. Math. Soc. 327 (1991), 329-351 Request permission
Abstract:
We generalize the Newton polygon procedure for algebraic equations to generate solutions of polynomial differential equations of the form $\sum \nolimits _{i = 0}^\infty {{\alpha _i}{x^{{\beta _i}}}}$ where the ${\alpha _i}$ are complex numbers and the ${\beta _i}$ are real numbers with ${\beta _0} > {\beta _1} > \cdots$. Using the differential version of the Newton polygon process, we show that any such a series solution is finitely determined and show how one can enumerate all such solutions of a given polynomial differential equation. We also show that the question of deciding if a system of polynomial differential equations has such a power series solution is undecidable.References
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Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 327 (1991), 329-351
- MSC: Primary 12H05; Secondary 12D15
- DOI: https://doi.org/10.1090/S0002-9947-1991-1012519-2
- MathSciNet review: 1012519