‎in this paper‎, ‎we construct a new iterative method for solving nonlinear volterra integral equation of second kind‎, ‎by approximating the legendre polynomial basis‎. ‎error analysis is worked using banach fixed point theorem‎. ‎we compute the approximate solution without using numerical method‎. ‎finally‎, ‎some examples are given to compare the results with some of the existing methods‎.

For the past two decades, the Volterra series reduced-order modeling approach has been successfully used for the purpose of flutter prediction, aeroelastic control design, and aeroelastic design optimization. The approach has been less successful, however, when applied to other important aeroelastic phenomena, such as aerodynamically induced limit-cycle oscillations. Similar to the Taylor serie...

Boundary control of nonlinear parabolic PDEs is an open problem with applications that include fluids, thermal, chemically-reacting, and plasma systems. In this paper we present stabilizing control designs for a broad class of nonlinear parabolic PDEs in 1-D. Our approach is a direct infinite dimensional extension of the finite-dimensional feedback linearization/backstepping approaches and empl...

A response approximation method for stochastically excited, nonlinear, dynamic systems is presented. Herein, the output of the nonlinear system is approximated by a finite-order Volterra series. The original nonlinear system is replaced by a bilinear system in order to determine the kernels of this Volterra series. The parameters of the bilinear system are determined by minimizing the differenc...

This paper deals with the identification and the control of nonlinear processes described by input -output models, such as parametric Volterra models. In particular, we extend an adaptive predictive algorithm without taking into account constraints. The calculation of the control law can be posed as a thirdorder nonlinear program. The building algorithm is based on a new approach using a convol...

This paper deals with the identification and the control of nonlinear processes described by input -output models, such as parametric Volterra models. In particular, we extend an adaptive predictive algorithm without taking into account constraints. The calculation of the control law can be posed as a thirdorder nonlinear program. The building algorithm is based on a new approach using a convol...

A new solution for the problem of selecting poles of the two-parameter Kautz functions in Volterra models is proposed. In general, a large number of parameters are required to represent the Volterra kernels, although this difficulty can be overcome by describing each kernel using a basis of orthonormal functions, such as the Kautz basis. This representation has a Wiener structure consisting of ...

The objective of this paper is t o present a new structure f o r an adaptive nonlinear equalizer f o r digital transmission over a nonlinear satellite channel with PSK modulation. The adaptive nonlinear equalizer is based o n a discrete frequencydomain third-order Volterra filter with the multidimensional overlap-save filtering technique, and o n the block least mean square (BLMS) algorithm f o...

The semidiscretization in space of Volterra-Fredholm integral equations (arising, for example, as mathematical models of the spreading of epidemics) leads to large systems of Volterra integral equations. Here, we study inexpensive timestepping methods using certain DQ (= direct quadrature) methods which are employed in a way that exploits the local superconvergence properties of spatial colloca...