Abstract: In this paper, we have proposed a numerical method
for solving fuzzy Fredholm integral equation of the second kind. In
this method a combination of orthonormal Bernstein and Block-Pulse
functions are used. In most cases, the proposed method leads to
the exact solution. The advantages of this method are shown by an
example and calculate the error analysis.
Abstract: In this paper, a new method for solution of second order linear Fredholm integral equation in power series form was studied. The result is obtained by using Banach fixed point theorem.
Abstract: This article is concerned with the determination of the static interaction of a vertically loaded rigid circular disc embedded at the interface of a horizontal layer sandwiched in between two different transversely isotropic half-spaces called as tri-material full-space. The axes of symmetry of different regions are assumed to be normal to the horizontal interfaces and parallel to the movement direction. With the use of a potential function method, and by implementing Hankel integral transforms in the radial direction, the government partial differential equation for the solely scalar potential function is transformed to an ordinary 4th order differential equation, and the mixed boundary conditions are transformed into a pair of integral equations called dual integral equations, which can be reduced to a Fredholm integral equation of the second kind, which is solved analytically. Then, the displacements and stresses are given in the form of improper line integrals, which is due to inverse Hankel integral transforms. It is shown that the present solutions are in exact agreement with the existing solutions for a homogeneous full-space with transversely isotropic material. To confirm the accuracy of the numerical evaluation of the integrals involved, the numerical results are compared with the solutions exists for the homogeneous full-space. Then, some different cases with different degrees of material anisotropy are compared to portray the effect of degree of anisotropy.
Abstract: We consider nonlinear uncertain systems such that a
priori information of the uncertainties is not available. For such
systems, we assume that the upper bound of the uncertainties is
represented as a Fredholm integral equation of the first kind and we
propose an adaptation law that is capable of estimating the upper
bound and design a continuous robust control which renders nonlinear
uncertain systems ultimately bounded.
Abstract: In this paper, application of the complexity reduction approach based on half- and quarter-sweep iteration concepts with Jacobi iterative method for solving composite trapezoidal (CT) algebraic equations is discussed. The performances of the methods for CT algebraic equations are comparatively studied by their application in solving linear Fredholm integral equations of the second kind. Furthermore, computational complexity analysis and numerical results for three test problems are also included in order to verify performance of the methods.
Abstract: In this paper first, a numerical method based on quasiinterpolation for solving nonlinear Fredholm integral equations of the Hammerstein-type is presented. Then, we approximate the solution of Hammerstein integral equations by Nystrom’s method. Also, we compare the methods with some numerical examples.
Abstract: in this paper, we propose a numerical method
for the approximate solution of fuzzy Fredholm functional
integral equations of the second kind by using an iterative
interpolation. For this purpose, we convert the linear fuzzy
Fredholm integral equations to a crisp linear system of integral
equations. The proposed method is illustrated by some fuzzy
integral equations in numerical examples.
Abstract: A numerical method for solving nonlinear Fredholm integral equations of second kind is proposed. The Fredholm type equations which have many applications in mathematical physics are then considered. The method is based on hybrid function approximations. The properties of hybrid of block-pulse functions and Chebyshev polynomials are presented and are utilized to reduce the computation of nonlinear Fredholm integral equations to a system of nonlinear. Some numerical examples are selected to illustrate the effectiveness and simplicity of the method.
Abstract: Sinc-collocation scheme is one of the new techniques
used in solving numerical problems involving integral equations. This
method has been shown to be a powerful numerical tool for finding
fast and accurate solutions. So, in this paper, some properties of the
Sinc-collocation method required for our subsequent development
are given and are utilized to reduce integral equation of the first
kind to some algebraic equations. Then convergence with exponential
rate is proved by a theorem to guarantee applicability of numerical
technique. Finally, numerical examples are included to demonstrate
the validity and applicability of the technique.
Abstract: In this paper we introduce an approach via optimization methods to find approximate solutions for nonlinear Fredholm integral equations of the first kind. To
this purpose, we consider two stages of approximation.
First we convert the integral equation to a moment problem and then we modify the new problem to two classes of optimization problems, non-constraint optimization problems
and optimal control problems. Finally numerical examples is
proposed.