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A second-derivative functionally fitted method of maximal order for oscillatory initial value problems

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Abstract

This paper deals with the construction of a functionally fitted method for solving first-order differential systems whose solutions present an oscillatory behaviour. The method incorporates the second derivative to obtain better accuracies and is developed on the basis that it provides no errors when the true solution is a linear combination of some trigonometric and exponential functions containing a parameter. The main properties of the method are presented, showing a fourth-order convergence. Some numerical experiments are included to show the good performance of the proposed method.

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Funding

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

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Authors and Affiliations

  1. Distance Learning institute, University of Lagos, Lagos, Nigeria

    R. I. Abdulganiy

  2. Department of Mathematics, University of Lagos, Lagos, Nigeria

    O. A. Akinfenwa & S. A. Okunuga

  3. Department of Applied Mathematics, Universidad de Salamanca, Salamanca, Spain

    H. Ramos

Authors
  1. R. I. Abdulganiy
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  2. O. A. Akinfenwa
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  3. H. Ramos
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  4. S. A. Okunuga
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Correspondence to R. I. Abdulganiy.

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Communicated by Jose Alberto Cuminato.

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Abdulganiy, R.I., Akinfenwa, O.A., Ramos, H. et al. A second-derivative functionally fitted method of maximal order for oscillatory initial value problems. Comp. Appl. Math. 40, 188 (2021). https://doi.org/10.1007/s40314-021-01582-8

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  • DOI: https://doi.org/10.1007/s40314-021-01582-8

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