scholarly journals The Telegraph Equation and Its Solution by Reduced Differential Transform Method

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Vineet K. Srivastava ◽  
Mukesh K. Awasthi ◽  
R. K. Chaurasia ◽  
M. Tamsir
Keyword(s):  
Telegraph Equation ◽  
Differential Transform Method ◽  
Mathematical Technique ◽  
Science And Engineering ◽  
Transform Method ◽  
Numerical Examples ◽  
One Dimensional ◽  
Wide Range ◽  
Differential Transform ◽  
Reduced Differential Transform Method

One-dimensional second-order hyperbolic telegraph equation was formulated using Ohm’s law and solved by a recent and reliable semianalytic method, namely, the reduced differential transform method (RDTM). Using this method, it is possible to find the exact solution or a closed approximate solution of a differential equation. Three numerical examples have been carried out in order to check the effectiveness, the accuracy, and convergence of the method. The RDTM is a powerful mathematical technique for solving wide range of problems arising in science and engineering fields.

scholarly journals Approximate Analytical Solution of One-Dimensional Beam Equations by Using Time-Fractional Reduced Differential Transform Method

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Dessalegn Mekonnen Yadeta ◽  
Ademe Kebede Gizaw ◽  
Yesuf Obsie Mussa
Keyword(s):  
Initial Conditions ◽  
Convergent Series ◽  
Differential Transform Method ◽  
Beam Equation ◽  
Transform Method ◽  
One Dimensional ◽  
Beam Equations ◽  
Differential Transform ◽  
Convergent Method ◽  
Reduced Differential Transform Method

In this paper, a recent and reliable method, named the fractional reduced differential transform method (FRDTM) is employed to solve one-dimensional time-fractional Beam equation subject to the appropriate initial conditions. This method provides the solutions very accurately and efficiently in convergent series form with easily computable coefficients. The efficacy and accuracy of this method are verified by means of three illustrative examples which indicate that the present method is very effective, simple, and easy to implement. Finally, it is observed that the FRDTM is the prevailing and convergent method for the solutions of linear and nonlinear fractional-order partial differential equations.

scholarly journals A modification of the reduced differential transform method for fractional calculus

2018 ◽  
Vol 22 (4) ◽  
pp. 1871-1875 ◽  
Author(s):  
Kang-Le Wang ◽  
Kang-Jia Wang
Keyword(s):  
Heat Transfer ◽  
Fractional Calculus ◽  
Differential Transform Method ◽  
New Method ◽  
Transform Method ◽  
Numerical Examples ◽  
Differential Transform ◽  
Transfer Equations ◽  
Reduced Differential Transform Method

In this paper, the reduced differential transform method is modified and successfully used to solve the fractional heat transfer equations. The numerical examples show that the new method is efficient, simple, and accurate.

scholarly journals NUMERICAL SOLUTION FOR TIME-FRACTIONAL MURRAY REACTION-DIFFUSION EQUATIONS VIA REDUCED DIFFERENTIAL TRANSFORM METHOD

2021 ◽  
Author(s):  
Muhammed Yiğider ◽  
Serkan Okur
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Fractional Differential Equations ◽  
Differential Transform Method ◽  
Reaction Diffusion Equations ◽  
Transform Method ◽  
Differential Transform ◽  
Fractional Differential ◽  
Reduced Differential Transform Method ◽  
Time Fractional Differential Equations

In this study, solutions of time-fractional differential equations that emerge from science and engineering have been investigated by employing reduced differential transform method. Initially, the definition of the derivatives with fractional order and their important features are given. Afterwards, by employing the Caputo derivative, reduced differential transform method has been introduced. Finally, the numerical solutions of the fractional order Murray equation have been obtained by utilizing reduced differential transform method and results have been compared through graphs and tables. Keywords: Time-fractional differential equations, Reduced differential transform methods, Murray equations, Caputo fractional derivative.

scholarly journals Solving a Higher-Dimensional Time-Fractional Diffusion Equation via the Fractional Reduced Differential Transform Method

2021 ◽  
Vol 5 (4) ◽  
pp. 168
Author(s):  
Salah Abuasad ◽  
Saleh Alshammari ◽  
Adil Al-rabtah ◽  
Ishak Hashim
Keyword(s):  
Approximate Solutions ◽  
Fractional Diffusion ◽  
Differential Transform Method ◽  
Diffusion Equations ◽  
Caputo Fractional Derivatives ◽  
Transform Method ◽  
Fractional Diffusion Equations ◽  
Higher Dimensional ◽  
Differential Transform ◽  
Reduced Differential Transform Method

In this study, exact and approximate solutions of higher-dimensional time-fractional diffusion equations were obtained using a relatively new method, the fractional reduced differential transform method (FRDTM). The exact solutions can be found with the benefit of a special function, and we applied Caputo fractional derivatives in this method. The numerical results and graphical representations specified that the proposed method is very effective for solving fractional diffusion equations in higher dimensions.

scholarly journals Approximate Analytic Solutions of Two-Dimensional Nonlinear Klein–Gordon Equation by Using the Reduced Differential Transform Method

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Wayinhareg Gashaw Belayeh ◽  
Yesuf Obsie Mussa ◽  
Ademe Kebede Gizaw
Keyword(s):  
Numerical Solutions ◽  
Initial Conditions ◽  
Type Systems ◽  
Analytical Approximation ◽  
Differential Transform Method ◽  
Two Dimensional ◽  
Transform Method ◽  
Differential Transform ◽  
Klein Gordon ◽  
Reduced Differential Transform Method

In this paper, the reduced differential transform method (RDTM) is successfully implemented for solving two-dimensional nonlinear Klein–Gordon equations (NLKGEs) with quadratic and cubic nonlinearities subject to appropriate initial conditions. The proposed technique has the advantage of producing an analytical approximation in a convergent power series form with a reduced number of calculable terms. Two test examples from mathematical physics are discussed to illustrate the validity and efficiency of the method. In addition, numerical solutions of the test examples are presented graphically to show the reliability and accuracy of the method. Also, the results indicate that the introduced method is promising for solving other type systems of NLPDEs.

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