A novel class of Obrechkoff-type methods for solving boundary value problems

Authors

  • Sunday Emmanuel Fadugba
    Department of Mathematics, Faculty of Physical Sciences, Ekiti State University, Ado-Ekiti, 360001, Nigeria.
  • Taiwo Eniola Fayode
    Department of Mathematical Sciences, Bamidele Olumilua University of Education, Science and Technology, Ikere
  • Malesela Clifford Kekana
    Department of Mathematics and Statistics, Tshwane University of Technology, Pretoria, South Africa

Keywords:

Obrechkoff-type methods, boundary value problem, second-order differential equation, numerical method, stability analysis

Abstract

A new family of high-order Obrechkoff-type block methods for the direct solution of second-order boundary value problems is proposed in this study. To discretize the differential equations, the methods are built using piecewise linear and constant approaches, as well as interpolation and collocation techniques based on Hermite splines of both first and higher orders. They are further developed using truncated power series expansions, achieving eighth order accuracy with favourable stability properties. The method captures key characteristics of the problem and is computationally efficient. A thorough theoretical analysis confirms that it is consistent, convergent, and zero-stable. A single illustrative example is considered and comparison with the well-known Runge–Kutta method demonstrates its superiority in accuracy and error reduction.

Dimensions

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Published

2026-04-20

How to Cite

A novel class of Obrechkoff-type methods for solving boundary value problems. (2026). Proceedings of the Nigerian Society of Physical Sciences, 305. https://doi.org/10.61298/pnspsc.2026..305

Issue

Volume 3, NSPS-ABU Conference, Feb. 9 - 14, 2026

Section

Articles
Copyright & Licensing

Copyright (c) 2026 Sunday Emmanuel Fadugba, Taiwo Eniola Fayode, Malesela Clifford Kekana (Author)

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

A novel class of Obrechkoff-type methods for solving boundary value problems. (2026). Proceedings of the Nigerian Society of Physical Sciences, 305. https://doi.org/10.61298/pnspsc.2026..305