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KIAM Preprint № 36, Moscow, 2011
Authors: Bruno A. D.
Exponential expansions of solutions to an ODE
Abstract:
We consider an ordinary differential equation of a very general form. Let we have found a power expansion of its solution with exponential addendums. In Section 1 we show how the addendums can be prolongated in the exponential expansions of solutions to the initial equation.We explain a method of calculation of critical numbers. Their absence is sufficient for the existence of the expansions. In section 2 we show a method for calculation of exponential expansions of solutions corresponding to a horisontal edge of the polygon of the equation. In Section 3 we proof statements of Sections 1 and 2. Examples from the Painlev´e equations are given.
Publication language: russian,  pages: 16
Research direction:
Mathematical problems and theory of numerical methods
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About authors:
  • Bruno Alexander Dmitrievich,  orcid.org/0000-0002-7465-1258KIAM RAS