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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 for of the solution. Two examples are provided.

Suggested Citation

  • M. De la Sen & A. Ibeas & R. Nistal, 2014. "Approximate Solutions by Truncated Taylor Series Expansions of Nonlinear Differential Equations and Related Shadowing Property with Applications," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-17, July.
    • Handle: RePEc:hin:jnlaaa:956318
    DOI: 10.1155/2014/956318
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