scholarly journals Reduced Differential Transform Method for Solving Linear and Nonlinear Goursat Problem

2016 ◽  
Vol 07 (10) ◽  
pp. 1049-1056
Author(s):  
Sharaf Mohmoud ◽  
Mohamed Gubara
Keyword(s):  
Goursat Problem ◽  
Differential Transform Method ◽  
Transform Method ◽  
Differential Transform ◽  
Linear And Nonlinear ◽  
Reduced Differential Transform Method

scholarly journals A Numerical Computation of a System of Linear and Nonlinear Time Dependent Partial Differential Equations Using Reduced Differential Transform Method

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Brajesh Kumar Singh ◽  
Mahendra
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Differential Transform Method ◽  
Time Dependent ◽  
Test Problems ◽  
Partial Differential ◽  
Transform Method ◽  
Differential Transform ◽  
Linear And Nonlinear ◽  
Reduced Differential Transform Method

This paper deals with an analytical solution of an initial value system of time dependent linear and nonlinear partial differential equations by implementing reduced differential transform (RDT) method. The effectiveness and the convergence of RDT method are tested by means of five test problems, which indicates the validity and great potential of the reduced differential transform method for solving system of partial differential equations.

scholarly journals Solving three-dimensional Volterra integral equation by the reduced differential transform method

2016 ◽  
Vol 5 (2) ◽  
pp. 103 ◽  
Author(s):  
Abdelhalim Ziqan ◽  
Sawsan Armiti ◽  
Iyad Suwan
Keyword(s):  
Integral Equation ◽  
Volterra Integral Equation ◽  
Three Dimensional ◽  
Differential Transform Method ◽  
Transform Method ◽  
Nonlinear Volterra Integral Equation ◽  
Differential Transform ◽  
Linear And Nonlinear ◽  
Reduced Differential Transform Method ◽  
Number Of Iterations

<p>In this article, the results of two-dimensional reduced differential transform method is extended to three-dimensional case for solving three dimensional Volterra integral equation. Using the described method, the exact solution can be obtained after a few number of iterations. Moreover, examples on both linear and nonlinear Volterra integral equation are carried out to illustrate the efficiency and the accuracy of the presented method.</p>

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

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Seyyedeh Roodabeh Moosavi Noori ◽  
Nasir Taghizadeh
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Nonlinear Problems ◽  
Differential Transform Method ◽  
System Of Differential Equations ◽  
Transform Method ◽  
Convergence Results ◽  
Differential Transform ◽  
Linear And Nonlinear ◽  
Reduced Differential Transform Method

In this work, we study the sufficient condition for convergence of the reduced differential transform method for nonlinear differential equations. The main power of this method is its ability and flexibility in solving linear and nonlinear problems properly and easily and obtain solutions both numerically and analytically. Simple approaches of reduced differential transform method and the convergence results for different classes of differential equations such as linear and nonlinear ordinary, partial, fractional, and system of differential equations are briefly discussed. Eight examples are checked to confirm convergence results as well as the strength and efficiency of the method.

scholarly journals Modified differential transform method for solving linear and nonlinear pantograph type of differential and Volterra integro-differential equations with proportional delays

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Seyyedeh Roodabeh Moosavi Noori ◽  
Nasir Taghizadeh
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Differential Transform Method ◽  
Hybrid Technique ◽  
Transform Method ◽  
Proportional Delays ◽  
Differential Transform ◽  
Computational Work ◽  
Linear And Nonlinear ◽  
First Time

AbstractIn this study, a hybrid technique for improving the differential transform method (DTM), namely the modified differential transform method (MDTM) expressed as a combination of the differential transform method, Laplace transforms, and the Padé approximant (LPDTM) is employed for the first time to ascertain exact solutions of linear and nonlinear pantograph type of differential and Volterra integro-differential equations (DEs and VIDEs) with proportional delays. The advantage of this method is its simple and trusty procedure, it solves the equations straightforward and directly without requiring large computational work, perturbations or linearization, and enlarges the domain of convergence, and leads to the exact solution. Also, to validate the reliability and efficiency of the method, some examples and numerical results are provided.

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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