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KIAM Preprint № 94, Moscow, 2013
Authors: Bruno A. D., Goryuchkina I. V.
Convergence of power expansions of solutions to an ODE
We consider an ordinary differential equation, containing variables and derivatives in real powers and its formal solutions in form of the asymptotic expansions in complex powers of independent variable with constant coefficients. We describe a way of proof of the convergence these expansions under condition that the order of derivative in the leading operator of the equation is equal to the order of the equation.
Convergence, algebraic ODEs, formal solutions, analytic functions
Publication language: russian,  pages: 16
Research direction:
Mathematical problems and theory of numerical methods
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About authors:
  • Bruno Alexander Dmitrievich, RAS
  • Goryuchkina I. V.,  KIAM RAS