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.

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

Main Subjects

• Mathematic