Author(s)

Serdar Beji

Faculty of Naval Architecture and Ocean Engineering, Istanbul Technical University, Istanbul, Türkiye.

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.

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

Beji, S. (2024) New Numerical Integration Formulations for Ordinary Differential Equations. Advances in Pure Mathematics, 14, 650-666. doi: 10.4236/apm.2024.148036.