Search results for " integral equation"
showing 10 items of 66 documents
Localization and separation of solutions for Fredholm integral equations
2020
[EN] In this paper, we establish a qualitative study of nonlinear Fredholm integral equations, where we will carry out a study on the localization and separation of solutions. Moreover, we consider an efficient algorithm to approximate a solution. To do this, we study the semilocal convergence of an efficient third order iterative scheme for solving nonlinear Fredholm integral equations under mild conditions. The novelty of our work lies in the fact that this study involves first order Frechet derivative and mild conditions. A numerical example involving nonlinear Fredholm integral equations, is solved to show the domains of existence and uniqueness of solutions. The applicability of the it…
Fractional Derivatives in Interval Analysis
2017
In this paper, interval fractional derivatives are presented. We consider uncertainty in both the order and the argument of the fractional operator. The approach proposed takes advantage of the property of Fourier and Laplace transforms with respect to the translation operator, in order to first define integral transform of interval functions. Subsequently, the main interval fractional integrals and derivatives, such as the Riemann–Liouville, Caputo, and Riesz, are defined based on their properties with respect to integral transforms. Moreover, uncertain-but-bounded linear fractional dynamical systems, relevant in modeling fractional viscoelasticity, excited by zero-mean stationary Gaussian…
An Advanced Numerical Model in Solving Thin-Wire Integral Equations by Using Semi-Orthogonal Compactly Supported Spline Wavelets
2003
Abstract—In this paper, the semi-orthogonal compactly sup- ported spline wavelets are used as basis functions for the efficient solution of the thin-wire electric field integral equation (EFIE) in frequency domain. The method of moments (MoM) is used via the Galerkin procedure. Conventional MoM directly applied to the EFIE, leads to dense matrix which often becomes computation- ally intractable when large-scale problems are approached. To overcome these difficulties, wavelets can be used as a basis set so obtaining the generation of a sparse matrix; this is due to the local supports and the vanishing moments properties of the wavelets. In the paper, this technique is applied to analyze elec…
A simulation model for electromagnetic transients in lightning protection systems
2002
This paper deals with the evaluation of electromagnetic transients in a lightning protection system (LPS). A field approach is used, based on the numerical solution of a modified version of the thin-wire electric field integral equation in the frequency domain. Time profiles of interesting electromagnetic quantities are computed by using a discrete fast Fourier transform algorithm. The model takes into account coupling effects among aerial parts and ground electrodes in order to correctly estimate the quantities which can determine electromagnetic hazard inside the LPS; transient touch and step voltages can be easily evaluated also taking into account the human body presence on the soil sur…
Intensive wave power and steel quenching 3-D model for cylindrical sample. Time direct and reverse formulations and solutions
2017
In this paper we develop mathematical models for three dimensional hyperbolic heat equations (wave equation or telegraph equation) with inner source power and construct their analytical solutions for the determination of the initial heat flux for cylindrical sample. As additional conditions the temperature and heat flux at the end time are given. In some cases we give expression of wave energy. In some cases we give expression of wave energy. Some solutions of time inverse problems are obtained in the form of first kind Fredholm integral equation, but others has been obtained in closed analytical form as series. We viewed both direct and inverse problems at the time. For the time inverse pr…
Alternative boundary integral equations for fracture mechanics in 2D anisotropic bodies
2017
An alternative dual boundary element formulation for generally anisotropic linear elastic twodimensional bodies is presented in this contribution. The formulation is based on the decomposition of the displacement field into the sum of a vector field satisfying the anisotropic Laplace equation and the gradient of the classic Airy stress function. By suitable manipulation of the integral representation of the anisotropic Laplace equation, a set of alternative integral equations is obtained, which can be used in combination with the displacement boundary integral equation for the solution of crack problems. Such boundary integral equations have the advantage of avoiding hyper-singular integral…
A fixed point theorem for G-monotone multivalued mapping with application to nonlinear integral equations
2017
We extend notion and theorem of [21] to the case of a multivalued mapping defined on a metric space endowed with a finite number of graphs. We also construct an example to show the generality of our result over existing results. Finally, we give an application to nonlinear integral equations
A spectral approach to a constrained optimization problem for the Helmholtz equation in unbounded domains
2014
We study some convergence issues for a recent approach to the problem of transparent boundary conditions for the Helmholtz equation in unbounded domains (Ciraolo et al. in J Comput Phys 246:78–95, 2013) where the index of refraction is not required to be constant at infinity. The approach is based on the minimization of an integral functional, which arises from an integral formulation of the radiation condition at infinity. In this paper, we implement a Fourier–Chebyshev collocation method to study some convergence properties of the numerical algorithm; in particular, we give numerical evidence of some convergence estimates available in the literature (Ciraolo in Helmholtz equation in unbou…
Low frequency gray-body factors and infrared divergences: rigorous results
2015
Formal solutions to the mode equations for both spherically symmetric black holes and Bose-Einstein condensate acoustic black holes are obtained by writing the spatial part of the mode equation as a linear Volterra integral equation of the second kind. The solutions work for a massless minimally coupled scalar field in the s-wave or zero angular momentum sector for a spherically symmetric black hole and in the longitudinal sector of a 1D Bose-Einstein condensate acoustic black hole. These solutions are used to obtain in a rigorous way analytic expressions for the scattering coefficients and gray-body factors in the zero frequency limit. They are also used to study the infrared behaviors of …
Wavelet-like bases for thin-wire integral equations in electromagnetics
2005
AbstractIn this paper, wavelets are used in solving, by the method of moments, a modified version of the thin-wire electric field integral equation, in frequency domain. The time domain electromagnetic quantities, are obtained by using the inverse discrete fast Fourier transform. The retarded scalar electric and vector magnetic potentials are employed in order to obtain the integral formulation. The discretized model generated by applying the direct method of moments via point-matching procedure, results in a linear system with a dense matrix which have to be solved for each frequency of the Fourier spectrum of the time domain impressed source. Therefore, orthogonal wavelet-like basis trans…