We investigate the well posedness of the stationary linear Boltzmann equation with space periodic electric field. We discuss the different behaviors that occur depending if the average electric field vanishes or not. The existence follows by perturbation techniques and stability arguments under uniform a priori estimates. The uniqueness of the weak solution holds for space periodic electric fie...

In this paper, we present a new formulation for the analysis of electromagnetic scattering from arbitrarily shaped threedimensional (3-D) perfectly conducting and piecewise homogeneous dielectric composite body. The formulation treated here is the combined field integral equation (CFIE). The conducting/dielectric structure is approximated by planar triangular patches, which have the ability to ...

urysohn integral equation is one of the most applicable topics in both pure and applied mathematics. the main objective of this paper is to solve the urysohn type fredholm integral equation. to do this, we approximate the solution of the problem by substituting a suitable truncated series of the well known legendre polynomials instead of the known function. after discretization of the problem o...

A novel diagonalized multilevel fast multipole method (MLFMM) for time harmonic Maxwell’s equations is proposed which realizes considerable memory savings without compromising accuracy and computational speed. The improvement is achieved by expanding the k-space integrals over the unit sphere in spherical harmonics. Since the spherical harmonics expansion is carried out for cartesian vector com...

The paper deals with the integral equation approach to steady kinematic dynamo models in finite domains based on Biot-Savart’s law. The role of the electric potential at the boundary is worked out explicitly. As an example, a modified version of the simple spherical α-effect dynamo model proposed by Krause and Steenbeck is considered in which the α-coefficient is no longer constant but may vary...

in this paper we consider a nonlinear two-phase stefan problem in one-dimensional space. the problem is mapped into a nonlinear volterra integral equation for the free boundary.

The energy content of electrostatic perturbations about homogeneous equilibria is discussed. The calculation leading to the well-known dielectric (or as it is sometimes called, the wave) energy is revisited and interpreted in light of Vlasov theory. It is argued that this quantity is deficient because resonant particles are not correctly handled. A linear integral transform is presented that so...

In this paper, a method-of-moments integral-equation formulation of a generalized scattering matrix (GSM) is presented for the full-wave analysis of interactive planar electric and magnetic discontinuities in waveguide. This was developed to efficiently handle a variety of waveguide-based strip-to-slot transitions, especially on thin substrates. This single matrix formulation replaces the probl...

in this paper, a nonlinear volterra-fredholm integral equation of the first kind is solved by using the homotopy analysis method (ham). in this case, the first kind integral equation can be reduced to the second kind integral equation which can be solved by ham. the approximate solution of this equation is calculated in the form of a series which its components are computed easily. the accuracy...