This paper presents a comparison between variational iteration method (VIM) and modfied variational iteration method (MVIM) for approximate solution a system of Volterra integral equation of the first kind. We convert a system of Volterra integral equations to a system of Volterra integro-di®erential equations that use VIM and MVIM to approximate solution of this system and hence obtain an appr...

In this paper, we study the existence of solutions of some nonlinear Volterra integral equations by using the techniques of measures of noncompactness and the Petryshyn's fixed point theorem in Banach space. We also present some examples of the integral equation to confirm the efficiency of our results.

in this paper, we propose the chebyshev wavelet approximation for the numerical solution of a class of integro-differential equation which describes the charged particle motion for certain configurations of oscillating magnetic fields. we show that the chebyshev approximation transform an integral equation to an explicit system of linear algebraic equations. illustrative examples are included t...

in this paper, shielding effectiveness (se) of a perforated enclosure with imperfectly conducting walls is evaluated. to this end, first, an accurate numerical technique based on method of moments (mom) ispresented. in this method, lossy metallic walls of the enclosure are replaced by equivalent electric surfacecurrent sources. then, the impedance boundary condition on the imperfectly conductin...

An integral symmetric matrix S = (sij) ∈ M sym m (Z) with sii ∈ 2Z gives rise to an integral quadratic form q(x) = 12 xSx on Z. If S is positive definite, the number r(q, t) of solutions x ∈ Z of the equation q(x) = t is finite, and it is one of the classical tasks of number theory to study the qualitative question which numbers t are represented by q or the quantitative problem to determine th...

A combination of recently developed techniques is applied to the collinear H2+H reaction. The techniques include combination of real regular finite range solutions of the Schrtdinger equation to form the scattering solution and the evaluation of the S matrix by projection at a set of configuration points. Favorable features like the 'energy-independent integral' techniques for wave function gen...

This guide describes a collection of programs for creating and re ning triangulations on surfaces and solving integral equations using collocation methods over these tri angulations The main purpose of this package is to allow for experimentation with numerical methods for solving boundary integral equations that are de ned on piecewise smooth surfaces in R For a general survey of the numerical...

where (x(£),x(0) = 0,0fktfíl\ is a Brownian motion process. Equation (0.1) has been studied by S. Bernstein [l], J. L. Doob [5] and others [2], [ 10]. In general, the solution given here is different from that given by these authors. Equation (0.1) is almost purely formal since the derivative dx/dt fails to exist with probability one. In [2], [5], [ 10], the stochastic integral of K. Ito [7], [...

Assume that $mathbb{D}$ is the open unit disk. Applying Ozaki's conditions, we consider two classes of locally univalent, which denote by $mathcal{G}(alpha)$ and $mathcal{F}(mu)$ as follows begin{equation*}  mathcal{G}(alpha):=left{fin mathcal{A}:mathfrak{Re}left( 1+frac{zf^{prime prime }(z)}{f^{prime }(z)}right) <1+frac{alpha }{2},quad 0<alphaleq1right}, end{equation*} and begin{equation*}  ma...

Let (Xt, t ≥ 0) be a Lévy process started at 0, with Lévy measure ν, and Tx the first hitting time of level x > 0 : Tx := inf {t ≥ 0; Xt > x}. Let F (θ, μ, ρ, .) be the joint Laplace transform of (Tx,Kx, Lx) : F (θ, μ, ρ, x) := E ( e1l{Tx<+∞} ) , where θ ≥ 0, μ ≥ 0, ρ ≥ 0, x ≥ 0, Kx := XTx − x and Lx := x−XT x − . If ν(R) < +∞ and ∫ +∞ 1 eν(dy) < +∞ for some s > 0, then we prove that F (θ, μ, ρ...