The Mohanad Transforms and Their Applications for Solving Systems of Differential Equations

IF 1 Q1 MATHEMATICS
Rania Saadeh, Al-anoud Alshawabkeh, Raed Khalil, Mohamed A. Abdoon, Nidal E. Taha, Dalal Khalid Almutairi
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引用次数: 1

Abstract

In recent years, Mohanad transform, a mathematical approach, has drawn a lot of interest from researchers. It is useful for solving many engineering and scientific problems, such as those involving electric circuits, population growth, vibrational beams, and heat conduction. The Mohanad transform is defined and introduced in this study, along with its fundamental qualities,including linearity and convolution. It is also discussed in connection with other integral transforms and how it is used in derivatives. Additionally, we use the Mohanad transform to solve a few systems of ordinary differential equations (ODEs) and review its properties in this paper. Determining the concentration of a chemical reactant (material) in a series is a physical chemistry problem that we use in the application part. We achieve this by developing a model based on ordinary differential equations (ODEs) and then solving them using the Mohanad transform. This research proves that, with little computational effort, we can get the exact solutions of ordinary differential equations (ODEs) via the Mohanad transform. We used graphs and tables to show our answer.
莫汉纳德变换及其在求解微分方程系统中的应用
近年来,莫哈纳德变换这一数学方法引起了研究人员的极大兴趣。它有助于解决许多工程和科学问题,如涉及电路、人口增长、振动波束和热传导的问题。本研究定义并介绍了莫汉纳德变换及其基本特性,包括线性和卷积。我们还将讨论它与其他积分变换的联系,以及它在导数中的应用。此外,我们还使用莫哈纳德变换求解了几个常微分方程(ODE)系统,并在本文中回顾了它的特性。确定一系列化学反应物(材料)的浓度是我们在应用部分使用的物理化学问题。为此,我们开发了一个基于常微分方程 (ODE) 的模型,然后使用莫哈纳德变换对其进行求解。这项研究证明,只需很少的计算量,我们就能通过莫汉纳德变换得到常微分方程的精确解。我们使用图形和表格来展示我们的答案。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
1.30
自引率
28.60%
发文量
156
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