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Trigonometrically fitted two-step hybrid methods for special second order ordinary differential equations

Author

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  • D’Ambrosio, R.
  • Ferro, M.
  • Paternoster, B.

Abstract

The purpose of this paper is to derive two-step hybrid methods for second order ordinary differential equations with oscillatory or periodic solutions. We show the constructive technique of methods based on trigonometric and mixed polynomial fitting and consider the linear stability analysis of such methods. We then carry out some numerical experiments underlining the properties of the derived classes of methods.

Suggested Citation

  • D’Ambrosio, R. & Ferro, M. & Paternoster, B., 2011. "Trigonometrically fitted two-step hybrid methods for special second order ordinary differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(5), pages 1068-1084.
    • Handle: RePEc:eee:matcom:v:81:y:2011:i:5:p:1068-1084
    DOI: 10.1016/j.matcom.2010.10.011
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    Cited by:

    1. Cardone, A. & Ixaru, L.Gr. & Paternoster, B. & Santomauro, G., 2015. "Ef-Gaussian direct quadrature methods for Volterra integral equations with periodic solution," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 110(C), pages 125-143.
    2. Franco, J.M. & Gómez, I., 2014. "Trigonometrically fitted nonlinear two-step methods for solving second order oscillatory IVPs," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 643-657.

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