Using of Two Dimensional HAAR Wavelet for Solving of Two Dimensional Nonlinear Fredholm Integral Equation

2017 ◽  
Vol 3 (2) ◽  
Keyword(s):  
Integral Equation ◽  
Fredholm Integral Equation ◽  
Haar Wavelet ◽  
Two Dimensional ◽  
Nonlinear Fredholm Integral Equation

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 Numerical Treatment of Fixed Point Applied to the Nonlinear Fredholm Integral Equation

2009 ◽  
Vol 2009 (1) ◽  
pp. 735638 ◽  
Author(s):  
MI Berenguer ◽  
MV Fernández Muñoz ◽  
AI Garralda Guillem ◽  
M Ruiz Galán
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fredholm Integral Equation ◽  
Numerical Treatment ◽  
Nonlinear Fredholm Integral Equation

scholarly journals SOME RAPIDLY CONVERGENT METHODS FOR NONLINEAR FREDHOLM INTEGRAL EQUATION

2005 ◽  
Vol 12 (1) ◽  
pp. 63-72
Author(s):  
I. Kaldo ◽  
O. Vaarmann
Keyword(s):  
Integral Equation ◽  
Fredholm Integral Equation ◽  
Inverse Operator ◽  
Iteration Process ◽  
Iteration Step ◽  
Nonlinear Fredholm Integral Equation ◽  
Computational Aspects ◽  
Iteration Methods ◽  
Fréchet Differentiable ◽  
Limited Accuracy

Many problems in modelling can be reduced to the solution of a nonlinear equation F(x) = 0, where F is a Frechet‐differentiable (as many times as necessary) mapping between Banach spaces X and Y. For solving this equation we consider high order iteration methods of the type xk +1 =xk ‐ Q(xk, Ai k ), i ∈ I, I = {1,…, r}, r ≥ 1, k = 0, 1, …, where Q(x, Ai k ) is an operator from X into itself and Ai k, i ∈ I, are some approximations to the inverse operator(s) occurring in the associated exact method. In particular, this set of methods contains methods with successive approximation of the inverse operator(s) and those based on the use of iterative methods to obtain a cheap solution of limited accuracy for corresponding linear equation(s) at each iteration step. A convergence theorem is proved and computational aspects of the methods under consideration are examined. The solution of nonlinear Fredholm integral equation by means of methods with convergence order p ≥ 2 are considered and possibilities of organizing parallel computation in iteration process are also briefly discussed. Daug modeliavimo problemu galima suformuluoti netiesines lygties F(x) = 0 pavidalu. Čia F yra Banacho erdves X atvaizdavimas i Banacho erdve Y, turintis visas reikalingas Freshe išvestines. Lygčiai F(x) = 0 spresti taikomas aukštosios eiles iteracinis procesas tokio tipo xk + 1 =xk ‐ Q(xk, Ai k ), i ∈ {1,…, r}, k = 0, 1, …, Čia Q(x, Ai k ) yra tam tikras operatorius X → X, Ai k , yra atvirkštinio atvaizdavimo aproksimacijos. Irodyta konvergavimo teorema ir išnagrineti metodu taikymo skaičiavimo aspektai. Aptariamos skaičiavimu lygiagretinimo galimybes, taikant si ulomus metodus netiesinei Fredholmo integralinei lygčiai.

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.

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