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.