Some Nonstandard Treatment of the Singularity in the Differential Equation

Document Type : Original Article

Authors
Mardan Ameen Pirdawood 1
Ibrahim Othman Hamad 2
1 Department of Mathematics, Faculty of Science and Health, Koya University, Koya KOY45, Kurdistan Region - F.R. Iraq.
2 Department of Mathematics, College of Science, Salahaddin University-Erbil, Hawler, Kurdistan Region - F.R. Iraq.
10.24271/psr.2022.161691
Abstract
This paper aims to use some non-standard concepts to find a non-standard analytic and non-analytic infinitely close solution of the first-order ordinary differential equation in the monad of its singularity, where the differential coefficients are either infinitesimal, unlimited or have basic differential form. The obtained non-standard solutions are more precise and compatible than the conventional ones. We named such a non-analytic infinitely close solution to the singularity by shadow solution. These cases of solutions are sometimes impossible to obtain by conventional methods.
Keywords
Nonstandard Analysis
Ordinary Differential Equation
S-Continuity
Singularity
Monad
Infinitesimal
Crossmark
Subjects
Passer Journal of Basic and Applied Sciences
Volume 4, Special issue
This special issue is related to the 9th Scientific Conference of University of Garmian: Pure Sciences and Technology Applications (SCUG-PSTA-2022) October 26–27, 2022. (All the manuscripts have been peer-reviewed.)
November 2022
Pages 142-159