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Exponentially Fitted and Trigonometrically Fitted Two-Derivative Runge-Kutta-Nyström Methods for Solving

Author

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  • Tahani Salama Mohamed
  • Norazak Senu
  • Zarina Bibi Ibrahim
  • Nik Mohd Asri Nik Long

Abstract

Two exponentially fitted and trigonometrically fitted explicit two-derivative Runge-Kutta-Nyström (TDRKN) methods are being constructed. Exponentially fitted and trigonometrically fitted TDRKN methods have the favorable feature that they integrate exactly second-order systems whose solutions are linear combinations of functions and respectively, when , the frequency of the problem. The results of numerical experiments showed that the new approaches are more efficient than existing methods in the literature.

Suggested Citation

  • Tahani Salama Mohamed & Norazak Senu & Zarina Bibi Ibrahim & Nik Mohd Asri Nik Long, 2018. "Exponentially Fitted and Trigonometrically Fitted Two-Derivative Runge-Kutta-Nyström Methods for Solving," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-19, September.
    • Handle: RePEc:hin:jnlmpe:7689854
    DOI: 10.1155/2018/7689854
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