Abstract:
An ordinary differential equation of quite general form is
considered. It is shown how to find the following near a
finite or infinite value of the independent variable by using
algorithms of power geometry: (i) all power-law asymptotic
expressions for solutions of the equation; (ii) all power-logarithmic
expansions of solutions with power-law asymptotics;
(iii) all non-power-law (exponential or logarithmic)
asymptotic expressions for solutions of the equation; (iv) certain
exponentially small additional terms for a power-logarithmic
expansion of a solution that correspond to exponentially close
solutions. Along with the theory and algorithms, examples are
presented of calculations of the above objects for one and the same equation.
The main attention is paid to explanations of algorithms
for these calculations.
Citation:
A. D. Bruno, “Asymptotic behaviour and expansions of solutions of an ordinary differential equation”, Russian Math. Surveys, 59:3 (2004), 429–480
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\by A.~D.~Bruno
\paper Asymptotic behaviour and expansions of solutions of an ordinary differential equation
\jour Russian Math. Surveys
\yr 2004
\vol 59
\issue 3
\pages 429--480
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\crossref{https://doi.org/10.1070/RM2004v059n03ABEH000736}
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Linking options:
https://www.mathnet.ru/eng/rm736
https://doi.org/10.1070/RM2004v059n03ABEH000736
https://www.mathnet.ru/eng/rm/v59/i3/p31
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