scholarly journals A Highly Efficient and Accurate Finite Iterative Method for Solving Linear Two-Dimensional Fredholm Fuzzy Integral Equations of the Second Kind Using Triangular Functions

2020 ◽  
Vol 2020 ◽  
pp. 1-16 ◽  
Author(s):  
Mohamed A. Ramadan ◽  
Heba S. Osheba ◽  
Adel R. Hadhoud
Keyword(s):  
Integral Equation ◽  
Fredholm Integral Equation ◽  
Equation System ◽  
Basis Functions ◽  
Computational Method ◽  
Fuzzy Integral ◽  
Two Dimensional ◽  
Orthogonal Functions ◽  
Triangular Form ◽  
Finite Iterative Method

This work introduces a computational method for solving the linear two-dimensional fuzzy Fredholm integral equation of the second form (2D-FFIE-2) based on triangular basis functions. We have used the parametric form of fuzzy functions and transformed a 2D-FFIE-2 with three variables in crisp case to a linear Fredholm integral equation of the second kind. First, a method based on the use of two m-sets of orthogonal functions of triangular form is implemented on the integral equation under study to be changed to coupled algebraic equation system. In order to solve these two schemes, a finite iterative algorithm is then applied to evaluate the coefficients that provided the approximate solution of the integral problems. Three examples are given to clarify the efficiency and accuracy of the method. The obtained numerical results are compared with other direct and exact solutions.

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.

A METHOD FOR MODELING THE RESISTIVITY AND IP RESPONSE OF TWO‐DIMENSIONAL BODIES

Geophysics ◽  
1976 ◽  
Vol 41 (5) ◽  
pp. 997-1015 ◽  
Author(s):  
Donald D. Snyder
Keyword(s):  
Integral Equation ◽  
Fourier Transform ◽  
Boundary Value Problem ◽  
Method Of Moments ◽  
Fredholm Integral Equation ◽  
Electric Potential ◽  
Inverse Fourier Transform ◽  
Two Dimensional ◽  
Numerical Techniques ◽  
Point Of Interest

A method has been developed for the solution of the resistivity and IP modeling problem for one or more two‐dimensional inhomogeneities buried in a space for which the Dirichlet Green’s function is known. The boundary‐value problem reduces to a Fredholm integral equation of the second kind which is parametrically a function of a spatial wavenumber. Using the method of moments, the integral equation is solved for a number of values of the wavenumber. An inverse Fourier transform is then performed in order to obtain the electric potential at any point of interest. The method agrees well with both experimental results and other numerical techniques.

scholarly journals Fractional Order Operational Matrix Method for Solving Two-Dimensional Nonlinear Fractional Volterra Integro-Differential Equations

2021 ◽  
Vol 45 (4) ◽  
pp. 571-585
Author(s):  
AMIRAHMAD KHAJEHNASIRI ◽  
◽  
M. AFSHAR KERMANI ◽  
REZZA EZZATI ◽  
◽  
...  
Keyword(s):  
Integral Equation ◽  
Differential Equations ◽  
Fractional Order ◽  
Volterra Integral Equation ◽  
Matrix Method ◽  
Operational Matrix ◽  
Basis Functions ◽  
Two Dimensional ◽  
Numerical Examples ◽  
Operational Matrix Method

This article presents a numerical method for solving nonlinear two-dimensional fractional Volterra integral equation. We derive the Hat basis functions operational matrix of the fractional order integration and use it to solve the two-dimensional fractional Volterra integro-differential equations. The method is described and illustrated with numerical examples. Also, we give the error analysis.

scholarly journals Total Ponderomotive Force on an Extended Test Body

2009 ◽  
Vol 2009 ◽  
pp. 1-12
Author(s):  
D. Langemann
Keyword(s):  
Integral Equation ◽  
Series Expansion ◽  
Fredholm Integral Equation ◽  
Ponderomotive Force ◽  
Test Body ◽  
Total Force ◽  
Two Dimensional ◽  
Insulating Material ◽  
Fourier Techniques ◽  
Numerical Effort

Droplets on insulating material suffer a nonvanishing total ponderomotive force because of the inhomogeneity of the surrounding electric field. A series expansion of this total force is proven in a two-dimensional setting by determining the line charge density at the boundary of the test body via a Fredholm integral equation, which is solved by Fourier techniques. The influence of electric charges in the neighborhood of the test body can be estimated as well as the convergence speed of the series expansion. In all realistic applications the series converges very fast. The numerical effort in the simulation of the motion of rainwater droplets on outdoor insulators reduces considerably.

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 Simple and Efficient Computational Method to Analyze Cylindrical Plasmonic Nanoantennas

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Karlo Costa ◽  
Victor Dmitriev
Keyword(s):  
Integral Equation ◽  
Electric Field ◽  
Method Of Moments ◽  
Surface Impedance ◽  
Near Infrared ◽  
Basis Functions ◽  
Computational Method ◽  
Good Precision ◽  
Cylindrical Structures ◽  
Plasmonic Nanoantennas

We present in this work a simple and efficient technique to analyze cylindrical plasmonic nanoantennas. In this method, we take into account only longitudinal current inside cylindrical structures and use 1D integral equation for the electric field with a given surface impedance of metal. The solution of this integral equation is obtained by the Method of Moments with sinusoidal basis functions. Some examples of calculations of nanoantennas with different geometries and sources are presented and compared with the commercial software Comsol 3D simulations. The results show that the proposed technique provides a good precision in the near-infrared and lower optical frequencies 100–400 THz.

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