in this paper, we present a new computational technique for solving nonlinear fredholm integral equations of the second kind. this proposed method is based on galerkin method and is computationally very attractive. moreover, for reducing the operations in comparing similar works, we design our algorithm based on transformations of orthogonal polynomials in approximation coefficients calculating...

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...

This paper develops a new method of integral sliding mode control redesign for a class of perturbed nonlinear dissipative switched systems by modifying the dissipativity-based control law that was designed for the unperturbed systems. The nominal model is considered affine with matched and unmatched perturbations. The redesigned control law includes an integral sliding-based control signal such...

In this paper, we propose a numerical method based on the generalized hat functions (GHFs) and improved hat functions (IHFs) to find numerical solutions for stochastic Volterra-Fredholm integral equation. To do so, all known and unknown functions are expanded in terms of basic functions and replaced in the original equation. The operational matrices of both basic functions are calculated and em...

1Landau Associates, 130 2nd Ave South, Edmonds, WA 98020, U.S.A. 2Civil and Environmental Engineering and National Center for Supercomputing Applications, University of Illinois at Urbana-Champaign, 205 North Mathews Ave Urbana, IL 61801, U.S.A. 3Department of Nuclear, Plasma and Radiological Engineering, University of Illinois at Urbana-Champaign, 216 Talbot Lab, 104 S. Wright St., Urbana, IL ...

The simulation of turbulent flows is an ongoing challenge. This is especially true for the flows in nuclear reactors. In order to save computational time and resource, accurate numerical schemes are required for such simulations. The encouraging results from the laminar flow simulations using Modified Nodal Integral Method (MNIM), serves as a motivation to use the method for turbulent flow simu...

A general theory is given for discretized versions of the Galerkin method for solving Fredholm integral equations of the second kind. The discretized Galerkin method is obtained from using numerical integration to evaluate the integrals occurring in the Galerkin method. The theoretical framework that is given parallels that of the regular Galerkin method, including the error analysis of the sup...

Recently, a new eigenvalue problem, called the transmission eigenvalue problem, has attracted many researchers. The problem arose in inverse scattering theory for inhomogeneous media and has important applications in a variety of inverse problems for target identification and nondestructive testing. The problem is numerically challenging because it is non-selfadjoint and nonlinear. In this pape...