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

Author

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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.

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, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:956318
    DOI: 10.1155/2014/956318
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    References listed on IDEAS

    as
    1. M. De la Sen & J. C. Soto & A. Ibeas, 2012. "Stability and Limit Oscillations of a Control Event-Based Sampling Criterion," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-25, June.
    2. Jaromír Baštinec & Leonid Berezansky & Josef Diblík & Zdeněk Šmarda, 2010. "On the Critical Case in Oscillation for Differential Equations with a Single Delay and with Several Delays," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
    3. Cemil Tunç & Melek Gözen, 2013. "Stability and Uniform Boundedness in Multidelay Functional Differential Equations of Third Order," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-7, May.
    4. Cemil Tunç & Melek Gözen, 2013. "Stability and Uniform Boundedness in Multidelay Functional Differential Equations of Third Order," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    5. Jaromír Baštinec & Leonid Berezansky & Josef Diblík & Zdeněk Šmarda, 2010. "On the Critical Case in Oscillation for Differential Equations with a Single Delay and with Several Delays," Abstract and Applied Analysis, Hindawi, vol. 2010, pages 1-20, September.
    6. M. De la Sen & J. C. Soto & A. Ibeas, 2012. "Stability and Limit Oscillations of a Control Event‐Based Sampling Criterion," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    Full references (including those not matched with items on IDEAS)

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