Improving the differential transform method: A novel technique to obtain the differential transforms of nonlinearities by the Adomian polynomials

Hooman Fatoorehchi; Hossein Abolghasemi

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Improving the differential transform method: A novel technique to obtain the differential transforms of nonlinearities by the Adomian polynomials

机译：改进微分变换方法：一种通过Adomian多项式获得非线性微分变换的新技术

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摘要

Although being powerful, the differential transform method (DTM) yet suffers from a drawback which is the lack of a systematic methodology for derivation of the differential transforms for nonlinear expressions. In the current paper, it is shown that this defect can be overcome with the help of the Adomian polynomials perfectly. The application of the proposed technique in treatment of nonlinear differential equations is well illustrated by a number of examples. In addition, the transformed analogues of some frequent nonlinearities are presented.

机译：尽管功能强大，但是差分变换方法（DTM）仍存在一个缺点，即缺少用于导出非线性表达式的差分变换的系统方法。在当前的论文中，表明可以借助Adomian多项式完美地克服此缺陷。许多示例很好地说明了所提出的技术在非线性微分方程处理中的应用。此外，还介绍了一些常见非线性的变换后的类似物。

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来源
《Applied Mathematical Modelling》 |2013年第8期|6008-6017|共10页
作者
Hooman Fatoorehchi; Hossein Abolghasemi;
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作者单位

Center for Separation Processes Modeling and Nano-Computations, School of Chemical Engineering, College of Engineering, University of Tehran, P.O. Box 11365-4563, Tehran, Iran;

Center for Separation Processes Modeling and Nano-Computations, School of Chemical Engineering, College of Engineering, University of Tehran, P.O. Box 11365-4563, Tehran, Iran,Oil and Gas Center of Excellence, University of Tehran, Tehran, Iran;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
Differential transform method; Nonlinearities; Adomian polynomials; Differential equations;

机译：差分变换法;非线性;Adomian多项式;微分方程;

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1. Nonlinear integro-differential equations by differential transform method with Adomian polynomials [J] . Australian Journal of Basic and Applied Sciences . 2013,第2013期

机译：非线性积分微分方程的Adomian多项式微分变换方法
2. Comparative study of Nonlinear partial differential equation using honotopy perturbation transform method (HPTM) using He's polynomial and mixture of Elzaki transform and partial differential transform method (PDTM) [J] . Indu Ratti International Journal of Applied Engineering Research . 2018,第18aPta4期

机译：利用HEATHOMIAL和ELZAKI变换和偏差变换方法（PDTM）多项式和混合物使用菱形扰动变换法（HPTM）非线性偏微分方程的比较研究（HPTM）（PDTM）
3. The Use of Variational Iteration Method, Differential Transform Method and Adomian Decomposition Method for Solving Different Types of Nonlinear Partial Differential Equations [J] . Necdet Bildik, Ali Konuralp International journal of nonlinear sciences and numerical simulation . 2006,第1期

机译：运用变分迭代法，微分变换法和Adomian分解法求解不同类型的非线性偏微分方程
4. Application of Differential Transform Method and Adomian Decomposition Method for Solving of one Nonlinear Boundary-Value-Transmission Problem [C] . Merve YüCEL, Oktay MUKHTAROV International Conference of Mathematical Sciences . 2019

机译：差分变换法和ADOMIAN分解方法解决一个非线性边界值传输问题的应用
5. Symbolic methods for analyzing polynomial and differential systems. [D] . Liang, Songxin. 2010

机译：分析多项式和微分系统的符号方法。
6. Solution of nonlinear higher-index Hessenberg DAEs by Adomian polynomials and differential transform method [O] . Brahim Benhammouda -1

机译：用Adomian多项式和微分变换法求解非线性高指数Hessenberg DAE
7. Nonlinear Integro-differential Equations by Differential Transform Method with Adomian Polynomials [O] . S. H. Behiry 2013

机译：具有adomian多项式的微分变换非线性积分微分方程

Improving the differential transform method: A novel technique to obtain the differential transforms of nonlinearities by the Adomian polynomials

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