Butcher, J.C. (2008) Numerical Methods for Ordinary Differential Equations. Wiley.
https://doi.org/10.1002/9780470753767

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.