scholarly journals An Approximate Solutions of two Dimension Linear Mixed Volterra- Fredholm Integral Equation of the Second Kind via Iterative Kernel Method

2019 ◽  
Vol 6 (2) ◽  
pp. 101-110
Author(s):  
Talaat Ismael Hasan
Keyword(s):  
Integral Equation ◽  
Exact Solution ◽  
Fredholm Integral Equation ◽  
Kernel Method ◽  
Approximate Solutions ◽  
Least Square ◽  
Computer Application ◽  
Numerical Examples ◽  
Running Time ◽  
Two Dimension

Abstract: In this work, we reformulate and apply iterative kernel method (IKM) for solving two dimension mixed Volterra-Fredholm integral equation of the second kind (MVFIE-2). The suitable algorithm for IKM is suggested and the programming for of the algorithm of the technique is written by Matlab programs. The computer application for the algorithm is tested on a number numerical examples. The results which are obtained by this technique compared with exact solution and some new theorems are proved; for decision the results computing the least square error (LSE) of the IKM and running time (RT) for the program.

scholarly journals Approximate Solution of Nonlinear Integral Equations of the Second Kind by Using Homotopy Perturbation Method

2017 ◽  
Vol 65 (2) ◽  
pp. 151-155
Author(s):  
MM Hasan ◽  
MA Matin
Keyword(s):  
Integral Equation ◽  
Exact Solution ◽  
Approximate Solution ◽  
Perturbation Method ◽  
Fredholm Integral Equation ◽  
Homotopy Perturbation Method ◽  
Nonlinear Integral Equations ◽  
Numerical Examples ◽  
Homotopy Perturbation ◽  
Nonlinear Fredholm Integral Equation

In this paper, we apply Homotopy perturbation method (HPM) for obtaining approximate solution of nonlinear Fredholm integral equation of the second kind. Finally, some numerical examples are provided, and the obtained numerical approximations are compared with the corresponding exact solution. Dhaka Univ. J. Sci. 65(2): 151-155, 2017 (July)

Numerical solution of two-dimensional first kind Fredholm integral equations by using linear Legendre wavelet

2016 ◽  
Vol 14 (01) ◽  
pp. 1650004 ◽  
Author(s):  
M. Tahami ◽  
A. Askari Hemmat ◽  
S. A. Yousefi
Keyword(s):  
Integral Equation ◽  
Tensor Product ◽  
Numerical Solution ◽  
Fredholm Integral Equation ◽  
Fredholm Integral Equations ◽  
Wavelet Basis ◽  
Two Dimensional ◽  
Legendre Wavelets ◽  
Numerical Examples ◽  
One Dimensional

In one-dimensional problems, the Legendre wavelets are good candidates for approximation. In this paper, we present a numerical method for solving two-dimensional first kind Fredholm integral equation. The method is based upon two-dimensional linear Legendre wavelet basis approximation. By applying tensor product of one-dimensional linear Legendre wavelet we construct a two-dimensional wavelet. Finally, we give some numerical examples.

scholarly journals A Triangle Algorithm of Padé-Type Approximant for Two-Dimensional Fredholm Integral Equations of the Second Kind

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Meilan Sun ◽  
Chuanqing Gu
Keyword(s):  
Integral Equation ◽  
Integral Equations ◽  
Fredholm Integral Equation ◽  
Recursive Algorithm ◽  
High Order ◽  
Fredholm Integral Equations ◽  
Two Dimensional ◽  
Initial Value ◽  
Numerical Examples ◽  
Type Approximation

The function-valued Padé-type approximation (2DFPTA) is used to solve two-dimensional Fredholm integral equation of the second kind. In order to compute 2DFPTA, a triangle recursive algorithm based on Sylvester identity is proposed. The advantage of this algorithm is that, in the process of calculating 2DFPTA to avoid the calculation of the determinant, it can start from the initial value, from low to high order, and gradually proceeds. Compared with the original two methods, the numerical examples show that the algorithm is effective.

scholarly journals Block-by-Block Method for Solving Nonlinear Volterra-Fredholm Integral Equation

2010 ◽  
Vol 2010 ◽  
pp. 1-8
Author(s):  
Abdallah A. Badr
Keyword(s):  
Integral Equation ◽  
Fredholm Integral Equation ◽  
Existence And Uniqueness ◽  
Time Dependent ◽  
Volterra Kernel ◽  
Block Method ◽  
Numerical Examples ◽  
Uniqueness Of The Solution ◽  
Fredholm Kernel

We consider a nonlinear Volterra-Fredholm integral equation (NVFIE) of the second kind. The Volterra kernel is time dependent, and the Fredholm kernel is position dependent. Existence and uniqueness of the solution to this equation, under certain conditions, are discussed. The block-by-block method is introduced to solve such equations numerically. Some numerical examples are given to illustrate our results.

scholarly journals A high order approach for nonlinear Volterra-Hammerstein integral equations

2021 ◽  
Vol 7 (1) ◽  
pp. 1460-1469
Author(s):  
Jian Zhang ◽  
◽  
Jinjiao Hou ◽  
Jing Niu ◽  
Ruifeng Xie ◽  
...  
Keyword(s):  
Integral Equation ◽  
Nonlinear Integral Equation ◽  
Homotopy Perturbation Method ◽  
Reproducing Kernel ◽  
Kernel Method ◽  
Linear Equations ◽  
Reproducing Kernel Method ◽  
Numerical Examples ◽  
Hammerstein Integral Equations ◽  
Homotopy Perturbation

<abstract><p>Here a scheme for solving the nonlinear integral equation of Volterra-Hammerstein type is given. We combine the related theories of homotopy perturbation method (HPM) with the simplified reproducing kernel method (SRKM). The nonlinear system can be transformed into linear equations by utilizing HPM. Based on the SRKM, we can solve these linear equations. Furthermore, we discuss convergence and error analysis of the HPM-SRKM. Finally, the feasibility of this method is verified by numerical examples.</p></abstract>

scholarly journals Application of Jacobi Polynomials to the Approximate Solution of a Singular Integral Equation with Cauchy Kernel on the Real Half-line

2006 ◽  
Vol 6 (3) ◽  
pp. 326-335
Author(s):  
D. Pylak
Keyword(s):  
Integral Equation ◽  
Exact Solution ◽  
Approximate Solution ◽  
Singular Integral Equation ◽  
Singular Integral ◽  
Jacobi Polynomials ◽  
Approximate Solutions ◽  
Half Line ◽  
Cauchy Kernel ◽  
The Real

AbstractIn this paper, exact solution of the characteristic equation with Cauchy kernel on the real half-line is presented. Next, Jacobi polynomials are used to derive approximate solutions of this equation. Moreover, estimations of errors of the approximated solutions are presented and proved.

Ship Centerplane Source Distribution

1980 ◽  
Vol 24 (01) ◽  
pp. 8-23
Author(s):  
T. Miloh ◽  
L. Landweber
Keyword(s):  
Experimental Data ◽  
Integral Equation ◽  
Exact Solution ◽  
Fredholm Integral Equation ◽  
Higher Order ◽  
Source Distribution ◽  
Line Integral ◽  
Irrotational Flow ◽  
Ship Model ◽  
Satisfactory Accuracy

A procedure for calculating the irrotational flow about a double ship model, by solving a Fredholm integral equation of the first kind for a centerplane source distribution, is described. The special problems of determining the curve in the centerplane bounding the source distribution and of smoothing sharply peaking inte-grands, to improve the accuracy of discretization of the integral equation, are treated. Application to ellipsoids, for which the results of the calculations can be compared with an exact solution, and to a ship form with parabolic lines, for which experimental data are available for comparison, indicate that satisfactory accuracy can be obtained by the method. A justification for using a centerplane distribution is that, as is shown, a line integral which appears in the higher-order solution for the flow about a ship form at nonzero Froude numbers can be avoided with such a distribution.

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