Study of Convergence of Reduced Differential Transform Method for Different Classes of Differential Equations

Taghizadeh, N.

doi:10.1155/2021/6696414

Cited by 17 publications

(13 citation statements)

References 31 publications

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“…This suggested technique is highly efficient and powerful in obtaining the exact solutions as well as approximate solutions of mathematical modeling of many problems in technology, finance, engineering disciplines, natural sciences such as biology, physics, chemistry, and earth science, gives the solution in the form of rapidly convergent successive approximations, and is capable of handling Linear and nonlinear equations in a similar manner. The basic definitions and operations of Two-dimensional reduced differential transform method [23][24][25][26][27] are introduced as follows.…”

Section: The Basic Ideas Of Reduced Differential Transform Methodmentioning

confidence: 99%

An analytical approximate method for solving unsteady state two-dimensional convection-diffusion equations

Al-Saif

Hasan

2022

JAM

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In this paper, an analytic approximate method for solving the unsteady two-dimensional convection-diffusion equations is introduced. Also, the convergence of the approximate methods is analyzed. Three test examples are presented, two have exact and one has not exacted solutions. The results obtained show that these methods are powerful mathematical tools for solving linear and nonlinear partial differential equations, moreover, new analytic Taylor method (NATM), reduced differential transform method (RDTM), and homotopy perturbation method (HPM), are more accurate and have less CPU time than the other methods.

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Section: The Basic Ideas Of Reduced Differential Transform Methodmentioning

confidence: 99%

An analytical approximate method for solving unsteady state two-dimensional convection-diffusion equations

Al-Saif

Hasan

2022

JAM

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“…Here we remark that DTM is rapidly convergent procedure. In this regards, various results related to convergence of the mentioned method for ODEs has been given in [33][34][35].…”

Section: Original Functionsmentioning

confidence: 99%

“…The method is rapidly convergent and this phenomenon has been proved in many articles. We refer in this regards some papers as [33][34][35].…”

Section: Introductionmentioning

confidence: 99%

Theory and Semi-Analytical Study of Micropolar Fluid Dynamics through a Porous Channel

Khan¹,

Ullah²,

Shah³

et al. 2023

Computer Modeling in Engineering &Amp; Sciences

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In this work, We are looking at the characteristics of micropolar flow in a porous channel that's being driven by suction or injection. The working of the fluid is described in the flow model. We can reduce the governing nonlinear partial differential equations (PDEs) to a model of coupled systems of nonlinear ordinary differential equations using similarity variables (ODEs). In order to obtain the results of a coupled system of nonlinear ODEs, we discuss a method which is known as the differential transform method (DTM). The concern transform is an excellent mathematical tool to obtain the analytical series solution to the nonlinear ODEs. To observe beast agreement between analytical method and numerical method, we compare our result with the Rung-Kutta method of order four (RK4). We also provide simulation plots to the obtained result by using Mathematica. On these plots, we discuss the effect of different parameters which arise during the calculation of the flow model equations.

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“…In 2009, the Turkish mathematician Keskin [8] proposed RDTM for the first time. It has drawn a lot of attention because several authors [9][10][11][12][13][14][15][16] have utilized it to find solutions to a variety of issues.Also the Yang transformation is suggested by Xiao-Jun Yang in 2016, which is applied to solve the steady heat transfer problem [17]. Henri Padé (1863-1953) presented an approximation technique in his doctoral thesis in 1892 which is called Padé approximation.…”

Section: -Introductionmentioning

confidence: 99%

A Hybrid Method with RDTM for Solving the Biological Population Model

2022

MTM

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In this paper, we establish an analytical solution to the non-linear biological population model using a hybrid method that combines a reduced differential transform method with a resummation method based on Yang transform and a Padé approximant. The proposed method significantly improves the approximate solution series and broadens the convergence field, It is also dependent on a few straightforward steps, and does not depend on a perturbation parameter or produce secular terms. Three examples are given to test the effectiveness, accuracy, and performance of the suggested method. The results and graph demonstrate that the suggested method is successful and more accurate than other methods. In addition, PYRDTM is a useful tool with great potential for solving nonlinear BPM.

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Study of Convergence of Reduced Differential Transform Method for Different Classes of Differential Equations

Cited by 17 publications

References 31 publications

An analytical approximate method for solving unsteady state two-dimensional convection-diffusion equations

An analytical approximate method for solving unsteady state two-dimensional convection-diffusion equations

Theory and Semi-Analytical Study of Micropolar Fluid Dynamics through a Porous Channel

A Hybrid Method with RDTM for Solving the Biological Population Model

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