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A trigonometrically fitted intra-step block Falkner method for the direct integration of second-order delay differential equations with oscillatory solutions

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Abstract

An intra-step block Falkner method whose coefficients depend on a parameter \(\omega \) and the step length h is presented in this study for solving numerically second-order delay differential equations with oscillatory solutions. In the development of the method, the collocation and interpolation techniques were employed. The investigation of the properties of the method has shown that it is zero-stable and consistent, and consequently, convergent. The application of the method to some standard problems from the scientific literature show that it produced very accurate results.

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

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Author notes

  1. R. I. Abdulganiy, H. Ramos, S. A. Okunuga and Z. Abdul Majid contributed equally to this work.

Authors and Affiliations

  1. Mathematics Unit, Department of Education, Distance Learning Institute, University of Lagos, Lagos Mainland, 101017, Lagos, Nigeria

    R. I. Abdulganiy

  2. Department of Applied Mathematics, Universidad de Salamanca, 37008, Salamanca, Spain

    H. Ramos

  3. Department of Mathematics, Faculty of Science, University of Lagos, Lagos Mainland, 101017, Lagos, Nigeria

    S. A. Okunuga

  4. Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, 43400, UPM Serdang, Malaysia

    Z. Abdul Majid

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  1. R. I. Abdulganiy
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  2. H. Ramos
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  4. Z. Abdul Majid
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Abdulganiy, R.I., Ramos, H., Okunuga, S. . et al. A trigonometrically fitted intra-step block Falkner method for the direct integration of second-order delay differential equations with oscillatory solutions. Afr. Mat. 34, 36 (2023). https://doi.org/10.1007/s13370-023-01075-3

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