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Signes-Pont, M.T., Boters-Pitarch, J., Cortés-Plana, J.J. and Mora-Mora, H. (2022) Approximating Ordinary Differential Equations by Means of the Chess Game Moves. Journal of Applied Mathematics and Physics, 10, 3240-3263.
https://doi.org/10.4236/jamp.2022.1010215

has been cited by the following article:

• TITLE: New Numerical Integration Formulations for Ordinary Differential Equations

  AUTHORS: Serdar Beji

  KEYWORDS: Single- and Multi-Step Numerical Integration, Unconventional Base-Functions, Ordinary Differential Equations

  JOURNAL NAME: Advances in Pure Mathematics, Vol.14 No.8, August 26, 2024

  ABSTRACT: An entirely new framework is established for developing various single- and multi-step formulations for the numerical integration of ordinary differential equations. Besides polynomials, unconventional base-functions with trigonometric and exponential terms satisfying different conditions are employed to generate a number of formulations. Performances of the new schemes are tested against well-known numerical integrators for selected test cases with quite satisfactory results. Convergence and stability issues of the new formulations are not addressed as the treatment of these aspects requires a separate work. The general approach introduced herein opens a wide vista for producing virtually unlimited number of formulations.