In this paper, the two-dimensional triangular orthogonal functions (2D-TFs) are applied for solving a class of nonlinear two-dimensional Volterra integral equations. 2D-TFs method transforms these integral equations into a system of linear algebraic equations. The high accuracy of this method is verified through a numerical example and comparison of the results with the other numerical methods.

In this paper, an iterative scheme for extracting approximate solutions of two dimensional Volterra-Fredholm integral equations is proposed. Considering some conditions on the kernel of the integral equation obtained by discretization of the integral equation, the convergence of the approximate solution to the exact solution is investigated. Several examples are provided to demonstrate the effi...

A bi-isotropic magneto-electric metamaterials is modeled by two independent reservoirs. The reservoirs contain a continuum of three dimensional harmonic oscillators, which describe polarizability and magnetizability of the medium. The paper aimed to investigate the effect of electromagnetic field on bi-isotropic. Starting with a total Lagrangian and using Euler-Lagrange equation, researcher cou...

We study singularity formation of three-dimensional ~3-D! vortex sheets without surface tension using a new approach. First, we derive a leading order approximation to the boundary integral equation governing the 3-D vortex sheet. This leading order equation captures the most singular contributions of the integral equation. By introducing an appropriate change of variables, we show that the lea...

The bound state Bethe-Salpeter amplitude was expressed by Nakanishi using a two-dimensional integral representation, in terms of a smooth weight function g, which carries the detailed dynamical information. A similar, but one-dimensional, integral representation can be obtained for the Light-Front wave function in terms of the same weight function g. By using the generalized Stieltjes transform...

It is shown that the inverse scattering problem for the three-dimensional SchrSdinger equation with a potential having no spherical symmetry can be solved using a Fredholm integral equation. The integral operator studied here is shown to be compact and self-adjoint with its spectrum in [-1, 1]. The relationship between solutions of this Fredholm equation and of a related RiemannHilbert problem ...