A class of Fredholm integral equations of the second kind, with respect to the exponential weight function w(x) = exp(-(x -α + x β )), α > 0, β > 1, on (0, +∞), is considered. The kernel k(x, y) and the function g(x) in such kind of... more
The paper deals with three-term recurrence relations for Boubaker and related polynomials, as well as some properties including zero distribution of such kinds of polynomials. Also, an application of these polynomials for obtaining... more
The paper deals with three-term recurrence relations for Boubaker and related polynomials, as well as some properties including zero distribution of such kinds of polynomials. Also, an application of these polynomials for obtaining... more
The paper deals with the approximation of the solution of the following bivariate Fredholm integral equation where the domain D is a triangle. The proposed procedure, by a suitable transformation, is essentially the Nyström method based... more
This paper present a numerical method for solving nonlinear Fredholm integral equations. The method is based upon Newton type approximations. Illustrative examples are included to demonstrate the validity and applicability of the technique.
In this paper we establish Gauss-type quadrature formulas for weakly singular integrals. An application of the quadrature scheme is given to obtain numerical solutions of the weakly singular Fredholm integral equation of the second kind.... more
This paper describes an effective strategy based on Lerch polynomial method for solving mixed integral equations (MIE) in position and time with a strongly symmetric singular kernel in the space L2(−1,1)×C[0,T],(T<1). The Quadratic... more
The purpose of this research is to explore a fixed point method to solve a class of functional equations, T u = f, where T is a differential or an integral operator on a Sobolev space H 2 (Ω), where Ω is an open set in R n . First, T is... more
In this article, two types of contractive conditions are introduced, namely extended integral Ϝ-contraction and (ϰ,Ω-Ϝ)-contraction. For the case of two mappings and their coincidence point theorems, a variant of (ϰ,Ω-Ϝ)-contraction has... more
In this study, using a one-dimensionl MRA we constructed a two-dimensional wavelet as well as four masks which are not related to the MRA. Finally, we provide some examples to prove the applicability of our construction in case of finding... more
A stochastic differential equation (SDE) is a differential equation in which one or more of the terms and the solution are stochastic processes. Numerous studies have employed orthogonal polynomials, however most of them focus on... more
In this paper, first, we propose an iterative method based on quadrature formula for solving two-dimensional linear fuzzy Fredholm integral equations (2DLFFIE). Then, we prove the error estimation of the method. In addition, we show the... more
In this paper, hybrid Bernstein polynomials and block-pulse functions based on the method of successive approximations are applied to obtain the approximate solution of nonlinear fuzzy Fredholm integral equations. The main idea of using... more
In this paper, by introducing a class of new orthogonal basis functions (NFs), we propose a numerical method to solve the nonlinear Volterra-Fredholm integral equations of the second kind (NVFIE2). To do this, first, we present the... more
In this paper, firstly, we review approximation of fuzzy functions by fuzzy bicubic splines interpolation and present a new approach based on the two-dimensional fuzzy splines interpolation and iterative method to approximate... more
In this paper, first, we apply the successive approximations method in terms of midpoint quadrature formula to solve nonlinear fuzzy Fredholm integral equations of the second kind (NFFIE-2). Considering some assumptions, we acquire a new... more
In this paper, a new approach to the numerical solution of Volterra-Fredholm integral equations by using CAS wavelets in combination with the collocation technique is proposed. First, the unknown function is approximated by using CAS... more
Nonlinear integral equations are studied in relation to vehicular traffic, biology, the theory of optimal control, economics, etc. In this paper, we use a numerical method for solving nonlinear Fredholm-Hammerstein integral equations by... more
In this paper, we propose an iterative procedure based on quadrature formula to solve nonlinear fuzzy Fredholm integral equations of the second kind. Moreover, the error estimation of the proposed method in terms of uniform and partial... more
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... more
In this paper we perform quantitative reconstruction of the electric susceptibility and the Grüneisen parameter of a non-magnetic linear dielectric medium using measurement of a multi-modal photoacoustic and optical coherence tomography... more
The use of carbon nanotubes as optical probes for scanning near-field optical microscopy requires an understanding of their near-field response. As a first step in this direction, we investigated the lateral resolution of a carbon... more
The problem of evaluating the information associated with Fredholm integral equations of the first kind, when the integral operator is selfadjoint and compact, is considered here. The data function is assumed to be perturbed gently by an... more
In this paper the problem of recovering a regularized solution of the Fredholm integral equations of the first kind with Hermitian and square-integrable kernels, and with data corrupted by additive noise, is considered. Instead of using a... more
The fuzzy transform setting (F-transform) is proposed as a tool for representation and approximation of type-1 and type-2 fuzzy numbers; the inverse F-transform on appropriate fuzzy partition of the membership interval [0,1] is used to... more
In this paper we obtain some results concerning the ascent and descent of a quasi-Fredholm relation in a Hilbert space and we analyze the behaviour of a polynomial in a quasi-Fredholm relation in a Hilbert space.
We introduce the concept of d-continuity and d-1-continuity for multivalued mappings defined on a partially ordered quasi-metric spaces. Then, we prove several fixed point theorems for multivalued maps which generalize the existing... more
In this paper, polynomial-based superconvergent degenerate kernel and Nyström methods for solving Fredholm integral equations of the second kind with the smooth kernel are studied. By using an interpolatory projection based on Legendre... more
The aim of this thesis is to provide a comprehensive study on Fredholm Integral Equations and the methods to find exact solutions. We also seek to present some effective methods to find the exact solutions for linear and nonlinear... more
Fredholm integral equations arise naturally in the context of ordinary and partial differential equations: Two-point boundary value problems can be reformulated as Fredholm integral equations, whose kernels are continuous but have finite... more
High accuracy numerical quadrature methods for integrals of singular periodic functions are proposed. These methods are based on the appropriate Euler-Maclaurin expansions of trapezoidal rule approximations and their extrapolations. They... more
A new solution to Maxwell's differential equations is proposed. A new approach for writing solutions to these equations under consideration uses quaternions. The equations are written as a kind of generalization of the Cauchy-Riemann... more
We study the Fredholm minors associated with a Fredholm equation of the second type. We present a couple of new linear recursion relations involving the nth and n -1th minors, whose solution is a representation of the nth minor as an n ×... more
In this paper we consider the velocity potential of water waves in the framework of linear theory.The circular plate lies on the free surface of water of finite depth with the circular obstacle far from it. The problem is reduced to a... more
We consider oscillations in cylindrical slotted resonators formed by combinations of rectangular domains with several slots cut in the walls using the methods of approximate semi-inversion of integral operator-valued functions with a... more
An adaptive method based on the trapezoidal rule for the numerical solution of Fredholm integral equations of the second kind is developed. The choice of mesh points is made automatically so as to equidistribute both the chauge in the... more
A general well function for groundwater flow toward an extraction well with non-uniform radial flux along the screen and finite-thickness skin, partially penetrating an unconfined, leaky-boundary flux, or confined aquifer is derived via... more
The present work proposes a numerical method to obtain an approximate solution of non-linear weakly singular Fredholm integral equations. The discrete Galerkin method in addition to thin-plate splines established on scattered points is... more
The purpose of this paper is to obtain a certain class of convolution integral equation of Fredholm type with the product of two generalized polynomials sets. Using of the Mellin transform technique; we have established solution of the... more
The coherent-mode representation (CMR) of an optical random source is a very powerful tool in contemporary optics. However, the practical value of the CMR is essentially restricted because of the complexity of solving the Fredholm... more
In this paper a method is proposed for solving the problem of the computation of the longitudinal coupling impedance for a particle which passes through the center of a round aperture in a perfectly conducting metallic plane (iris). It is... more
A method for numerical solution of Fredholm integral equations of the first kind is derived and illustrated The solution f(x) of the integral equation is assumed to be a sample function of a wide-sense stationary random process with known... more
In this study, a collocation method based on the Bessel polynomials is introduced for the approximate solutions of high-order linear Fredholm-Volterra integro-differential equations (FVIDEs) under mixed conditions. In addition, the method... more
In this paper, a numerical matrix method based on collocation points is presented for the approximate solution of the systems of high-order linear Fredholm integro-differential equations with variable coefficients under the mixed... more
In this study, a collocation method based on the Bessel polynomials is introduced for the approximate solutions of high-order linear Fredholm-Volterra integro-differential equations (FVIDEs) under mixed conditions. In addition, the method... more
This paper gives a regular vector boundary integral equation for solving the problem of viscous scattering of a pressure wave by a rigid body. Firstly, single-layer viscous potentials and a generalized stress tensor are introduced.... more
An efficient multigrid finite-differences scheme for solving elliptic Fredholm partial integro-differential equations (PIDE) is discussed. This scheme combines a second-order accurate finite difference discretization of the PIDE problem... more