New Numerical Integration Formulations for Ordinary Differential Equations  

作　　者：Serdar Beji Serdar Beji(Faculty of Naval Architecture and Ocean Engineering, Istanbul Technical University, Istanbul, Trkiye)

机构地区：[1]Faculty of Naval Architecture and Ocean Engineering, Istanbul Technical University, Istanbul, Trkiye

出　　处：《Advances in Pure Mathematics》2024年第8期650-666,共17页理论数学进展（英文）

摘　　要：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.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.

关 键 词：Single- and Multi-Step Numerical Integration Unconventional Base-Functions Ordinary Differential Equations 

分 类 号：O17[理学—数学]