We analyze well-posedness of a scattering problem of time-harmonic electromagnetic waves by periodic structures with sign-changing coefficients. Transmission problems for Maxwell’s equations with sign-changing coefficients in bounded domains have been recently studied by Bonnet-Ben Dhia and co-workers in the so-called T -coercivity framework. In this article we generalize such framework for per...

In this paper, a randomized numerical approach is used to obtain approximate solutions for a class of nonlinear Fredholm integral equations of the second kind. The proposed approach contains two steps: at first, we define a discretized form of the integral equation by quadrature formula methods and solution of this discretized form converges to the exact solution of the integral equation by con...

Since various problems in science and engineering fields can be modeled by nonlinear Volterra-Fredholm integral equations, the main focus of this study is to present an effective numerical method for solving them. This method is based on the hybrid functions of Legendre polynomials and block-pulse functions. By using this approach, a nonlinear Volterra-Fredholm integral equation reduces to a no...

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 system. We consider the mathematical model presented in [11], where a Fredholm integral equation of the first kind for the Grüneisen parameter was derived. For ...

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 approximate analytical solution of Love’s integral equation is presented. This Fredholm integral equation of the second kind appeared in an electrostatic problem ana...

This paper makes a short study of Fredholm integral equations related to potential theory and elasticity, with a view to preparing the ground for their exploitation in the numerical solution of difficult boundary-value problems. Attention is drawn to the advantages of Fredholm's first equation and of Green's boundary formula. The latter plays a fundamental and hitherto unrecognized role in the ...

April, 2005 Abstract. A model with wealth accumulation subject to i.i.d. random shocks is examined. The transfer function shows what kt+1 wealth at t+ 1 would be, given kt, with no shock. It has a positive slope, but indeterminate concavity/convexity. The stationary distribution satis…es a Fredholm integral equation and can be examined by direct analysis of the stochastic process or via the Fre...

The Fredholm–Volterra integral equation of the second kind with continuous kernels with respect to position and time, is solved numerically, using the Collocation and Galerkin methods. Also the error, in each case, is estimated.

We investigate the τ -function of the quadrilateral lattice using the nonlocal ∂̄-dressing method, and we show that it can be identified with the Fredholm determinant of the integral equation which naturally appears within that approach.