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Approximate solutions by truncated Taylor series expansions of nonlinear differential equations and related shadowing property with applications. (English) Zbl 1474.34077

Summary: This paper investigates the errors of the solutions as well as the shadowing property of a class of nonlinear differential equations which possess unique solutions on a certain interval for any admissible initial condition. The class of differential equations is assumed to be approximated by well-posed truncated Taylor series expansions up to a certain order obtained about certain, in general nonperiodic, sampling points \(t_i \in [t_0, t_J]\) for \(i = 0,1, \ldots, J\) of the solution. Two examples are provided.

MSC:

34A45 Theoretical approximation of solutions to ordinary differential equations
41A58 Series expansions (e.g., Taylor, Lidstone series, but not Fourier series)
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