Approximate solutions by truncated Taylor series expansions of nonlinear differential equations and related shadowing property with applications (Q1725377)

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.