Three-dimensional Differential Transform Method For Solving Nonlinear Three-dimensional Volterra Integral Equations

2012 ◽  
Vol 04 (02) ◽  
pp. 246-256 ◽  
Author(s):  
M. Bakhshi ◽  
M. Asghari-larimi ◽  
M. Asghari-larimi
Keyword(s):  
Integral Equations ◽  
Three Dimensional ◽  
Volterra Integral Equations ◽  
Differential Transform Method ◽  
Transform Method ◽  
Differential Transform

scholarly journals Solving Three Dimensions Volterra Integral Equations (TDVIE) via a Neural Network

2019 ◽  
Vol 23 (10) ◽  
pp. 92
Author(s):  
Nahdh S. M. Al-Saif ◽  
Ameen Sh. Ameen ◽  
Ghaith Fadhil Abbas2
Keyword(s):  
Neural Network ◽  
Integral Equations ◽  
Three Dimensional ◽  
Volterra Integral Equations ◽  
Three Dimensions ◽  
Feed Forward Neural Network ◽  
Transform Method ◽  
Linear Transfer Function ◽  
Differential Transform ◽  
Hidden Layer

The aim of this paper  is present a new numerical method for solvingThree Dimensions Volterra Integral Equations using artificial neural network by design multilayer feed forward Neural Network. A multi- layers design in our proposed method consist of a hidden layer having seven hidden units. and one linear output unit. Linear Transfer function used as each unit and using Levenberg- Marquardtalgorithmtraining. Moreover, examples on three- dimensional Volterra integral equations carried out to illustrate the accuracy and the efficiency of the presented method. In addition, some comparisons among proposed method and Shifted Chebyshev Polynomials method and Reduced Differential Transform Method are presented.   http://dx.doi.org/10.25130/tjps.23.2018.176

scholarly journals Differential transform method for solving singularly perturbed Volterra integral equations

2011 ◽  
Vol 23 (2) ◽  
pp. 223-228 ◽  
Author(s):  
Nurettin Doğan ◽  
Vedat Suat Ertürk ◽  
Shaher Momani ◽  
Ömer Akın ◽  
Ahmet Yıldırım
Keyword(s):  
Integral Equations ◽  
Volterra Integral Equations ◽  
Differential Transform Method ◽  
Singularly Perturbed ◽  
Transform Method ◽  
Differential Transform

scholarly journals Numerical Study of Two-Dimensional Volterra Integral Equations by RDTM and Comparison with DTM

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Reza Abazari ◽  
Adem Kılıçman
Keyword(s):  
Integral Equations ◽  
Numerical Study ◽  
Volterra Integral Equations ◽  
Differential Transform Method ◽  
The Other ◽  
Two Dimensional ◽  
Nonlinear Integral Equations ◽  
Transform Method ◽  
Engineering Sciences ◽  
Differential Transform

The two-dimensional Volterra integral equations are solved using more recent semianalytic method, the reduced differential transform method (the so-called RDTM), and compared with the differential transform method (DTM). The concepts of DTM and RDTM are briefly explained, and their application to the two-dimensional Volterra integral equations is studied. The results obtained by DTM and RDTM together are compared with exact solution. As an important result, it is depicted that the RDTM results are more accurate in comparison with those obtained by DTM applied to the same Volterra integral equations. The numerical results reveal that the RDTM is very effective, convenient, and quite accurate compared to the other kind of nonlinear integral equations. It is predicted that the RDTM can be found widely applicable in engineering sciences.

New Fractional Analytical Study of Three-Dimensional Evolution Equation Equipped With Three Memory Indices

2019 ◽  
Vol 14 (11) ◽  
Author(s):  
Feras Yousef ◽  
Marwan Alquran ◽  
Imad Jaradat ◽  
Shaher Momani ◽  
Dumitru Baleanu
Keyword(s):  
Analytical Study ◽  
Three Dimensional ◽  
Fractional Power ◽  
Differential Transform Method ◽  
Initial Value ◽  
Transform Method ◽  
Differential Transform ◽  
Fractional Models ◽  
Fractional Differential ◽  
Fractional Power Series

Abstract Herein, analytical solutions of three-dimensional (3D) diffusion, telegraph, and Burgers' models that are equipped with three memory indices are derived by using an innovative fractional generalization of the traditional differential transform method (DTM), namely, the threefold-fractional differential transform method (threefold-FDTM). This extends the applicability of DTM to comprise initial value problems in higher fractal spaces. The obtained solutions are expressed in the form of a γ¯-fractional power series which is a fractional adaptation of the classical Taylor series in several variables. Furthermore, the projection of these solutions into the integer space corresponds with the solutions of the classical copies for these models. The results detect that the suggested method is easy to implement, accurate, and very efficient in (non)linear fractional models. Thus, research on this trend is worth tracking.

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