This paper is concerned with the application of boundary integral equation method to the electromagnetic scattering of a perfect conductor in the three dimensional space. A collocation method is employed for the magnetic eld integral equation and error estimates are derived. Fareld patterns and radar cross sections are computed for various wave numbers in the case of sphere. Numerical experimen...

This paper presents an integral solution of the generalized one-dimensional equation of energy transport with the convective term. The solution of the problem has been achieved by the use of a novel technique that involves generalized derivatives (in particular, derivatives of noninteger orders). Confluent hypergeometric functions, known as Whittaker’s functions, appear in the course of the sol...

In this paper, we present an analysis of electromagnetic scattering from arbitrarily shaped three-dimensional (3D) conducting objects coated with dielectric materials. The integral equation treated here is the combined field integral equation (CFIE). The objective of this paper is to illustrate that only the CFIE formulation is a valid methodology in removing defects, which occur at a frequency...

Using an approach developed earlier for renormalization of the Boltzmann collision integral [Saveliev and Nanbu, Phys. Rev. E 65, 051205 (2002)], we derive an exact divergence form for the fragmentation operator. Then we reduce the fragmentation equation to the continuity equation in size space, with the flux given explicitly. This allows us to obtain self-similar solutions and to find the inte...

This paper presents to the solutions of the acoustic problem using dual reciprocity boundary element method (DRBEM). The acoustic propagates inside the silencer and its sound can be formulated by the three dimensional (3D) Helmholtz equation. The form of the equation is which can be solved by the integral form on the boundary. The conventional boundary element method (BEM) is not suitable for s...

and Applied Analysis 3 hard to obtain because they are highly nonlinear equations and most probably they are not integrable equations in general. Thus, large numbers of research results are still concentrated in the classical KdV equation and some other high-order equations with KdV type, such as KdV-Burgers equation [17, 18] and KdV-Burgers-Kuramoto equation [19], at present. Therefore, the in...

the first integral method is an efficient method for obtaining exact solutions of some nonlinear partial differential equations. this method can be applied to non integrable equations as well as to integrable ones. in this paper, the first integral method is used to construct exact solutions of the 2d ginzburg-landau equation.

in this paper, the bernstein polynomials are used to approximate the solutions of linear integral equations with multiple time lags (iemtl) through expansion methods (collocation method, partition method, galerkin method). the method is discussed in detail and illustrated by solving some numerical examples. comparison between the exact and approximated results obtained from these methods is...

in this paper, we present a computational method for solving boundary integral equations with loga-rithmic singular kernels which occur as reformulations of a boundary value problem for the laplacian equation. themethod is based on the use of the galerkin method with cas wavelets constructed on the unit interval as basis.this approach utilizes the non-uniform gauss-legendre quadrature rule for ...

In this paper we present a numerical solution method for the Bernoulli free boundary value problem for the Laplace equation in three dimensions. We extend a nonlinear integral equation approach for the free boundary reconstruction [21] from the two-dimensional to the three-dimensional case. The idea of the method consists in reformulating Bernoulli’s problem as a system of boundary integral equ...