Comparison of the Selected Methods Used for Solving the Ordinary Differential Equations and Their Systems

Edyta Hetmaniok and Mariusz Pleszczyński
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Edyta Hetmaniok: Faculty of Applied Mathematics, Silesian Technical University of Gliwice, 44-100 Gliwice, Slaskie, Poland
Mariusz Pleszczyński: Faculty of Applied Mathematics, Silesian Technical University of Gliwice, 44-100 Gliwice, Slaskie, Poland

Mathematics, 2022, vol. 10, issue 3, 1-15

Abstract: Ordinary differential equations (ODEs), and the systems of such equations, are used for describing many essential physical phenomena. Therefore, the ability to efficiently solve such tasks is important and desired. The goal of this paper is to compare three methods devoted to solving ODEs and their systems, with respect to the quality of obtained solutions, as well as the speed and reliability of working. These approaches are the classical and often applied Runge–Kutta method of order 4 (RK4), the method developed on the ground of the Taylor series, the differential transformation method (DTM), and the routine available in the Mathematica software (Mat).

Keywords: ordinary differential equations; Runge–Kutta method; differential transformation method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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