Methods in Mathematica for Solving Ordinary Differential Equations

Göktaş, Ünal; Kapadia, Devendra

doi:10.3390/mca16040784

Cited by 2 publications

(2 citation statements)

References 17 publications

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“…The order of a differential equation is governed by the order of the highest order derivative in the equation; according to its linearity, it can be a linear or nonlinear equation. The above is a simple summary of the principles or basic concepts of differential equations, from them, more concepts are derived, and obviously, the most important part of them is how to solve them and their applications, the reason for this study [1,8,9]. The applications that have been mostly studied are the analysis of relationships between quantities and their rates of change, which are frequent in areas such as Physics, Biology, Engineering, or Economics [10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Use of Ordinary Differential Equations Applied to Mechanical and Electrical Problems With First Order Linear Systems

Al¹

2023

RLJ

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In recent years there has been an increased interest in the study of mathematics applied to engineering to study aspects of its teaching. In the present research work, a compilation of analytical concepts of differential equations applied to the solution of problems of electrical circuits, a branch of electrical engineering and mechanical engineering problems, specifical problems of spring-mass mechanical systems, through the description of the analytical solutions of direct current electrical circuits and spring-mass mechanical systems, applying differential equations. This method stands out among the diverse mathematical treatments used to solve this type of engineering problem, both for its demonstrative elegance and capacity to offer a total answer. Likewise, practical engineering examples related to the studied subject were presented and the results were obtained and analyzed by using the mathematical software, Wolfram Mathematica.

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Section: Introductionmentioning

confidence: 99%

Use of Ordinary Differential Equations Applied to Mechanical and Electrical Problems With First Order Linear Systems

Al¹

2023

RLJ

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“…In this paper, we consider second-order ODEs, convert them to a system of ODEs and compare the exact and numerical solution. This exploration is investigated through evaluation using Mathematica® [6], [7], [8]. Euler's and Runge-Kutta [9], [5], [10] algorithm are implemented with its built-in function.…”

Section: Introductionmentioning

confidence: 99%

Numerical Investigation on System of Ordinary Differential Equations Absolute Time Inference with Mathematica®

Adeniji¹,

Samuel²,

Andrew³

et al. 2021

IJACSA

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The purpose of this research is to perform a comparative numerical analysis of an efficient numerical methods for second-order ordinary differential equations, by reducing the second-order ODE to a system of first-order differential equations. Then we obtain approximate solutions to the system of ODE. To validate the accuracy of the algorithm, a comparison between Euler's method and the Runge-Kutta method or order four was carried out and an exact solution was found to verify the efficiency, accuracy of the methods. Graphical representations of the parametric plots were also presented. Time inference analysis is taken to check the time taken to executes the algorithm in Mathematica®12.2.0. The obtained approximate solution using the algorithm shows that the Runge-Kutta method of order four is more efficient for solving system of linear ordinary differential equations.

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Methods in Mathematica for Solving Ordinary Differential Equations

Abstract: An overview of the solution methods for ordinary differential equations in the Mathematica function DSolve is presented.

Cited by 2 publications

References 17 publications

Use of Ordinary Differential Equations Applied to Mechanical and Electrical Problems With First Order Linear Systems

Use of Ordinary Differential Equations Applied to Mechanical and Electrical Problems With First Order Linear Systems

Numerical Investigation on System of Ordinary Differential Equations Absolute Time Inference with Mathematica®

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