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 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.

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.

Generalized Differential Transform Method for Solving RLC Electric Circuit of Non-Integer Order

2018 ◽  
Vol 7 (2) ◽  
pp. 127-135 ◽  
Author(s):  
N. Magesh ◽  
A. Saravanan
Keyword(s):  
Exact Solution ◽  
Initial Conditions ◽  
Electric Circuit ◽  
Convergent Series ◽  
Second Order ◽  
Differential Transform Method ◽  
Transform Method ◽  
Rlc Circuit ◽  
Differential Transform ◽  
Generalized Differential

AbstractSystematic construction of fractional ordinary differential equations [FODEs] has gained much attention nowadays research because dimensional homogeneity plays a major role in mathematical modeling. In order to keep up the dimension of the physical quantities, we need some auxiliary parameters. When we utilize auxiliary parameters, the FODE turns out to be more intricate. One of such kind of model is non-homogeneous fractional second order RLC circuit. To solve this kind of complicated FODEs, we need proficient modern analytical method. In this paper, we use two different methods, one is modern and the other is traditional, namely generalized differential transform Method (GDTM) and Laplace transform method (LTM) to obtain the analytical solution of non-homogeneous fractional second order RLC circuit. We present the solution in terms of convergent series. Though GDTM and LTM are capable to produce the exact solution of fractional RLC circuit, great strength of GDTM over LTM is that differential transform of initial conditions occupy the coefficients of first two terms in series solution so that we arrive exact solution with few iterations and also, it does not allow the noise terms while computing the coefficients. Due to this, GDTM takes less time to converge than LTM and it has been demonstrated. Furthermost, we discuss the characteristics of non-homogeneous fractional second order RLC circuit through numerical illustrations.

scholarly journals Modified Reduced Differential Transform Method for Partial Differential-Algebraic Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Brahim Benhammouda ◽  
Hector Vazquez-Leal ◽  
Arturo Sarmiento-Reyes
Keyword(s):  
Perturbation Parameter ◽  
Convergent Series ◽  
Differential Algebraic Equations ◽  
Differential Transform Method ◽  
Algebraic Equations ◽  
Partial Differential ◽  
Transform Method ◽  
Partial Differential Algebraic Equations ◽  
Differential Transform ◽  
Reduced Differential Transform Method

This work presents the application of the reduced differential transform method (RDTM) to find solutions of partial differential-algebraic equations (PDAEs). Two systems of index-two and index-three are solved to show that RDTM can provide analytical solutions for PDAEs in convergent series form. In addition, we present the posttreatment of the power series solutions with the Laplace-Padé resummation method as a useful technique to find exact solutions. The main advantage of the proposed technique is that it is based on a few straightforward steps and does not generate secular terms or depend on a perturbation parameter.

scholarly journals Modified Fractional Reduced Differential Transform Method for the Solution of Multiterm Time-Fractional Diffusion Equations

2019 ◽  
Vol 2019 ◽  
pp. 1-14 ◽  
Author(s):  
Salah Abuasad ◽  
Ishak Hashim ◽  
Samsul Ariffin Abdul Karim
Keyword(s):  
Initial Conditions ◽  
Approximate Solutions ◽  
Fractional Diffusion ◽  
Differential Transform Method ◽  
Diffusion Equations ◽  
Transform Method ◽  
Fractional Diffusion Equations ◽  
Fractional Equations ◽  
Differential Transform ◽  
Reduced Differential Transform Method

In this study, we introduce a new modification of fractional reduced differential transform method (m-FRDTM) to find exact and approximate solutions for nonhomogeneous linear multiterm time-fractional diffusion equations (MT-TFDEs) of constant coefficients in a bounded domain with suitable initial conditions. Different applications in two and three fractional order terms are given to illustrate our new modification. The approximate solutions are given in the form of series solutions. The results show that the m-FRDTM for MT-TFDEs is a powerful method and can be generalized to other types of multiterm time-fractional equations.

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.

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