Approximate Analytical Solution to Nonlinear Delay Differential Equations by Using Sumudu Iterative Method

IF 1 4区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL
Asfaw Tsegaye Moltot, Alemayehu Tamirie Deresse
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引用次数: 2

Abstract

In this study, an efficient analytical method called the Sumudu Iterative Method (SIM) is introduced to obtain the solutions for the nonlinear delay differential equation (NDDE). This technique is a mixture of the Sumudu transform method and the new iterative method. The Sumudu transform method is used in this approach to solve the equation’s linear portion, and the new iterative method’s successive iterative producers are used to solve the equation’s nonlinear portion. Some basic properties and theorems which help us to solve the governing problem using the suggested approach are revised. The benefit of this approach is that it solves the equations directly and reliably, without the prerequisite for perturbations or linearization or extensive computer labor. Five sample instances from the DDEs are given to confirm the method’s reliability and effectiveness, and the outcomes are compared with the exact solution with the assistance of tables and graphs after taking the sum of the first eight iterations of the approximate solution. Furthermore, the findings indicate that the recommended strategy is encouraging for solving other types of nonlinear delay differential equations.
非线性时滞微分方程的Sumudu迭代近似解析解
在本研究中,引入了一种有效的分析方法Sumudu迭代法(SIM)来获得非线性延迟微分方程(NDDE)的解。该技术是Sumudu变换方法和新迭代方法的混合。该方法使用Sumudu变换方法求解方程的线性部分,使用新迭代方法的逐次迭代生成器求解方程的非线性部分。修正了一些基本性质和定理,这些性质和定理有助于我们用所提出的方法解决控制问题。这种方法的好处是,它直接可靠地求解方程,而不需要扰动或线性化或大量的计算机工作。给出了DDE的五个样本实例,以证实该方法的可靠性和有效性,并在取近似解的前八次迭代之和后,借助表格和图表将结果与精确解进行比较。此外,研究结果表明,推荐的策略对于求解其他类型的非线性时滞微分方程是令人鼓舞的。
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
Advances in Mathematical Physics
Advances in Mathematical Physics 数学-应用数学
CiteScore
2.40
自引率
8.30%
发文量
151
审稿时长
>12 weeks
期刊介绍: Advances in Mathematical Physics publishes papers that seek to understand mathematical basis of physical phenomena, and solve problems in physics via mathematical approaches. The journal welcomes submissions from mathematical physicists, theoretical physicists, and mathematicians alike. As well as original research, Advances in Mathematical Physics also publishes focused review articles that examine the state of the art, identify emerging trends, and suggest future directions for developing fields.
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