Bounded solution of characteristic singular integral equation using differential transform method

2015 ◽  
Author(s):  
M. Abdulkawi ◽  
M. Y. H. Alyami
Keyword(s):  
Integral Equation ◽  
Singular Integral Equation ◽  
Singular Integral ◽  
Bounded Solution ◽  
Differential Transform Method ◽  
Transform Method ◽  
Differential Transform

scholarly journals Bounded solution of Cauchy type singular integral equation of the first kind using differential transform method

2018 ◽  
Vol 14 (1) ◽  
pp. 7580-7595
Author(s):  
M. Abdulkawi
Keyword(s):  
Integral Equation ◽  
Approximate Solution ◽  
Singular Integral Equation ◽  
Singular Integral ◽  
Singular Integrals ◽  
Bounded Solution ◽  
Differential Transform Method ◽  
Cauchy Type ◽  
Transform Method ◽  
Differential Transform

In this paper, an efficient approximate solution for solving the Cauchy type singular integral equation of the first kind is presented. Bounded solution of the Cauchy type singular Integral equation is discussed. Two type of kernel, separable and convolution, are considered. The differential transform method is used in the solution. New theorems for transformation of Cauchy singular integrals are given with proofs. Approximate results areshown to illustrate the efficiency and accuracy of the approximate solution.

scholarly journals Unbounded solution of characteristic singular integral equation using differential transform method

2014 ◽  
Vol 9 (7) ◽  
pp. 2869-2881 ◽  
Author(s):  
Mohammad Abdulkawi Mahiub
Keyword(s):  
Integral Equation ◽  
Singular Integral Equation ◽  
Singular Integral ◽  
Numerical Results ◽  
Differential Transform Method ◽  
Cauchy Type ◽  
Unbounded Solution ◽  
Transform Method ◽  
Present Solution ◽  
Differential Transform

In this paper, The differential transform method is extended to solve the Cauchy type singular integral equation of the first kind. Unbounded solution of the Cauchy type singular  Integral equation is discussed. Numerical results are shown to illustrate the efficiency and accuracy of the present solution.

scholarly journals Solution of Abel Integral Equation Using Differential Transform Method

2018 ◽  
Vol 14 (1) ◽  
pp. 7521-7532
Author(s):  
Subhabrata Mondal ◽  
B. N. Mandal
Keyword(s):  
Applied Sciences ◽  
Integral Equation ◽  
Fractional Order ◽  
Solid Mechanics ◽  
Differential Transform Method ◽  
Transform Method ◽  
Abel Integral Equation ◽  
Differential Transform ◽  
Abel Integral Equations ◽  
Fractional Differential

The application of fractional differential transform method, developed for differential equations of fractional order, are extended to derive exact analytical solutions of fractional order Abel integral equations. The fractional integrations are described in the Riemann-Liouville sense and fractional derivatives are described in the Caputo sense. Abel integral equation occurs in the mathematical modeling of various problems in physics, astrophysics, solid mechanics and applied sciences. An analytic technique for solving Abel integral equation of first kind by the proposed method is introduced here. Also illustrative examples with exact solutions are considered to show the validity and applicability of the proposed method. Abel integral equation, Differential transform method, Fractional differential transform method.

scholarly journals An Analytical and Approximate Solution for Nonlinear Volterra Partial Integro-Differential Equations with a Weakly Singular Kernel Using the Fractional Differential Transform Method

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Rezvan Ghoochani-Shirvan ◽  
Jafar Saberi-Nadjafi ◽  
Morteza Gachpazan
Keyword(s):  
Integral Equation ◽  
Differential Equations ◽  
Approximate Solutions ◽  
Differential Transform Method ◽  
Singular Kernel ◽  
Weakly Singular Kernel ◽  
Transform Method ◽  
Weakly Singular ◽  
Differential Transform ◽  
Fractional Differential

An analytical-approximate method is proposed for a type of nonlinear Volterra partial integro-differential equations with a weakly singular kernel. This method is based on the fractional differential transform method (FDTM). The approximate solutions of these equations are calculated in the form of a finite series with easily computable terms. The analytic solution is represented by an infinite series. We state and prove a theorem regarding an integral equation with a weak kernel by using the fractional differential transform method. The result of the theorem will be used to solve a weakly singular Volterra integral equation later on.

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>

Sign in / Sign up

Export Citation Format

Share Document