An integral equation approach with a new solution procedure using moment method (MoM) is applied for the computation of coupled currents on the surface of a printed dipole antenna and inside its high-permittivity three-dimensional dielectric substrate. The main purpose of this study is to validate the accuracy and reliability of the previously proposed MoM procedure by authors for the solution ...

in this paper, we present a method for solving the rst kind abel integral equation. in thismethod, the rst kind abel integral equation is transformed to the second kind volterraintegral equation with a continuous kernel and a smooth deriving term expressed by weaklysingular integrals. by using sidi's sinm - transformation and modied navot-simpson'sintegration rule, an algorithm for...

Abstract In this paper, the representation of the exact solution to the nonlinear Volterra-Fredholm integral equations will be obtained in the reproducing kernel space. The exact solution is represented in the form of series. Its approximate solution is obtained by truncating the series and a new numerical approximate method is obtained. The error of the approximate solution is monotone deceasi...

In this paper, a generalization of Nadler’s fixed point theorem is presented for H-type k-multivalued weak contractive mappings. We consider a nonconvex Hammerstein type integral inclusion and prove an existence theorem by using an H-type multi-valued weak contractive mapping.

Alternative Legendre polynomials (ALPs) are used to approximate the solution of a class of nonlinear Volterra-Hammerstein integral equations. For this purpose, the operational matrices of integration and the product for ALPs are derived. Then, using the collocation method, the considered problem is reduced into a set of nonlinear algebraic equations. The error analysis of the method is given an...

Arnold, Falk, and Winther recently showed [Bull. Amer. Math. Soc. 47 (2010), 281–354] that linear, mixed variational problems, and their numerical approximation by mixed finite element methods, can be studied using the powerful, abstract language of Hilbert complexes. In another recent article [arXiv:1005.4455], we extended the Arnold–Falk–Winther framework by analyzing variational crimes (a la...

We consider a class of two-dimensional integral equations with noncompact monotone Hammerstein operators and concave nonlinearity. prove constructive theorem on the existence uniqueness nontrivial nonnegative bounded solution study asymptotic behavior at infinity. Some examples kernels nonlinearity are given.