Notice of Retraction: Applications of differential transform method to linear volterra integral equations

2010 ◽  
Author(s):  
Khatereh Tabatabaei
Keyword(s):  
Integral Equations ◽  
Volterra Integral Equations ◽  
Differential Transform Method ◽  
Transform Method ◽  
Differential Transform ◽  
Linear Volterra Integral Equations

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.

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

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