Time-dependent problems that are modeled by initial-boundary value problems for parabolic or hyperbolic partial differential equations can be treated with the boundary integral equation method. The ideal situation is when the right-hand side in the partial differential equation and the initial conditions vanish, the data are given only on the boundary of the domain, the equation has constant co...

The analysis of transient scattering from perfectly conducting as well as potentially inhomogeneous penetrable bodies often is effected using marching on in time based time domain integral equation methods. This paper reviews the state of the art in the field, highlighting recent advances that address not only their stability and computational efficiency, but also their convergence and hybridiz...

In this paper, we present a new formulation using the ( ) time-domain electric-field integral equation TD EFIE to obtain a transient scattering response from arbitrarily shaped conducting bodies. The time deri ati e of the magnetic ector potential is approximated with a central finite difference, and the scalar potential is time a eraged by di iding it into two terms. This approach with an impl...

in this paper, we use a combination of legendre and block-pulse functionson the interval [0; 1] to solve the nonlinear integral equation of the second kind.the nonlinear part of the integral equation is approximated by hybrid legen-dre block-pulse functions, and the nonlinear integral equation is reduced to asystem of nonlinear equations. we give some numerical examples. to showapplicability of...

‎we study dual integral equations which appear in formulation of the‎ ‎potential distribution of an electrified plate with mixed boundary‎ ‎conditions‎. ‎these equations will be converted to a system of‎ ‎singular integral equations with cauchy type kernels‎. ‎using‎ ‎chebyshev polynomials‎, ‎we propose a method to approximate the‎ ‎solution of cauchy type singular integral equation which will ...

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...