在巴格利-托尔维克方程中利用改良阿多米分解法处理迪里夏特边界条件

IF 1 Q1 MATHEMATICS
M. Al-Mazmumy, Mona Alsulami
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引用次数: 0

摘要

Bagley-Torvik 方程是一个重要的微分方程,在数学物理和力学的各个分支中经常出现。然而,分析处理该模型的方法却寥寥无几;事实上,研究人员在研究中经常采用半分析和数值方法。因此,本研究的主要目标是找到符合 Dirichlet 边界数据的分数 Bagley-Torvik 方程以及分数 Bagley-Torvik 方程系统的精确解析解。因此,本研究旨在证明,通过所提出的两种算法,修正阿多米分解法(MADM)是处理一类具有 Dirichlet 边界数据的 Bagley-Torvik 方程的非常有效的方法。当然,MADM 是一种非常强大的方法,可用于求解不同的函数方程,而无需线性化、离散化、扰动甚至不必要的限制性假设。此外,只要可以获得精确的分析解,该方法就能揭示精确解;如果无法获得精确解,该方法也能揭示闭式数列解。最后,研究了一些治理模型的示例测试问题,以证明所提算法的优越性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Utilization of the Modified Adomian Decomposition Method on the Bagley-Torvik Equation Amidst Dirichlet Boundary Conditions
The Bagley-Torvik equation is an imperative differential equation that considerably arises in various branches of mathematical physics and mechanics. However, very few methods exist for the treatment of the model analytically; in fact, researchers frequently shop for semi-analytical and numerical methods in their studies. Therefore, the main goal of this research is to find theexact analytical solution for the fractional Bagley-Torvik equation fitted with Dirichlet boundary data, as well as a system of fractional Bagley-Torvik equations. Thus, this research aims to show that the modified Adomian decomposition method (MADM) via the proposed two algorithms is a very effective method for treating a class of Bagley-Torvik equations endowed with Dirichletboundary data. Certainly, MADM is a very powerful approach for solving dissimilar functional equations without the need for either linearization, discretization, perturbation, or even unnecessary restraining postulations. Additionally, the method reveals exact analytical solutions whenever obtainable or closed-form series solutions whenever exact solutions are not feasible. Lastly, some illustrative test problems of the governing model are examined to demonstrate the superiority of the proposed algorithms.
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来源期刊
CiteScore
1.30
自引率
28.60%
发文量
156
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