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Approximate Solutions by Truncated Taylor Series Expansions of Nonlinear Differential Equations and Related Shadowing Property with Applications

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  • M. De la Sen
  • A. Ibeas
  • R. Nistal

Abstract

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 ti ∈ [t0, tJ] for i = 0,1, …, J of the solution. Two examples are provided.

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Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:956318
DOI: 10.1155/2014/956318
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