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.

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 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.

Vibration of Elastic Structures With Cracks

1993 ◽  
Vol 60 (2) ◽  
pp. 414-421 ◽  
Author(s):  
I. Y. Shen
Keyword(s):  
Integral Equation ◽  
Fredholm Integral Equation ◽  
The Other ◽  
Internal Crack ◽  
Two Dimensional ◽  
Antiplane Strain ◽  
Elastic Solids ◽  
Helmholtz Operator ◽  
Crack Configuration ◽  
Analytical Algorithm

An analytical algorithm is proposed to represent eigensolutions [λm2, ψm(r)]m=1∞ of an imperfect structure C containing cracks in terms of crack configuration σc and eigensolutions [ωn2, φn(r)]n=1∞ of a perfect structured without P the cracks. To illustrate this algorithm on mechanical systems governed by the two-dimensional Helmholtz operator, the Green’s identity and Green’sfunction of P are used to represent ψm(r) in terms of an infinite series of φn(r). Substitution of the ψn(r) representation into the Kamke quotient of C and stationarity of the quotient result in a matrix Fredholm integral equation. The eigensolutions of the Fredholm integral equation then predict λm2 and ψm(r) of C. Finally, eigensolutions of two rectangular elastic solids under antiplane strain vibration, one with a boundary crack and the other with an oblique internal crack, are calculated numerically.

A novel technique based on Bernoulli wavelets for numerical solutions of two-dimensional Fredholm integral equation of second kind

2019 ◽  
Vol 36 (6) ◽  
pp. 1798-1819
Author(s):  
S. Saha Ray ◽  
S. Behera
Keyword(s):  
Integral Equation ◽  
Fredholm Integral Equation ◽  
Numerical Solutions ◽  
Bernoulli Polynomials ◽  
Fredholm Integral Equations ◽  
Two Dimensional ◽  
Algebraic Equations ◽  
Content Type ◽  
Good Convergence ◽  
Novel Technique

Purpose A novel technique based on Bernoulli wavelets has been proposed to solve two-dimensional Fredholm integral equation of second kind. Bernoulli wavelets have been created by dilation and translation of Bernoulli polynomials. This paper aims to introduce properties of Bernoulli wavelets and Bernoulli polynomials. Design/methodology/approach To solve the two-dimensional Fredholm integral equation of second kind, the proposed method has been used to transform the integral equation into a system of algebraic equations. Findings Numerical experiments shows that the proposed two-dimensional wavelets technique can give high-accurate solutions and good convergence rate. Originality/value The efficiency of newly developed two-dimensional wavelets technique has been validated by different illustrative numerical examples to solve two-dimensional Fredholm integral equations.

scholarly journals Numerical Solution of Two-Dimensional Linear Fuzzy Fredholm Integral Equations by the Fuzzy Lagrange Interpolation

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
H. Nouriani ◽  
R. Ezzati
Keyword(s):  
Integral Equation ◽  
Stability Analysis ◽  
Iterative Method ◽  
Fredholm Integral Equation ◽  
Numerical Stability ◽  
Lagrange Interpolation ◽  
Fredholm Integral Equations ◽  
Two Dimensional ◽  
New Approach ◽  
Numerical Stability Analysis

In this study, at first, we propose a new approach based on the two-dimensional fuzzy Lagrange interpolation and iterative method to approximate the solution of two-dimensional linear fuzzy Fredholm integral equation (2DLFFIE). Then, we prove convergence analysis and numerical stability analysis for the proposed numerical algorithm by two theorems. Finally, by some examples, we show the efficiency of the proposed method.

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