A class of nonlinear stochastic processes satysfying a Lipschitz-type strip condition and supplied by a linear output equation, is considered. Robust asymptotic (high-gain) state estimation for nonlinear stochastic processes via di erential neural networks is discussed. A new type learning law for the weight dynamics is suggested. By a stochastic Lyapunov-like analysis (with Ito formula impleme...

Algebraic integral equations is a special category of Volterra integral equations system,  that has many applications in physics and engineering. The principal aim of this paper is to serve the numerical solution of an integral algebraic equation by using the Taylor expansion method. In this method, using the Taylor expansion of the unknown function, the algebraic integral equation system becom...

In this study, an effective technique upon compactly supported semi orthogonal cubic Bspline wavelets for solving nonlinear Volterra-Fredholm integral equations is proposed. Properties of B-spline wavelets and function approximation by them are first presented and the exponential convergence rate of the approximation, Ο(2 -4j ), is proved. For solving the nonlinear Volterra-Fredholm integral eq...

In this paper, we studied the numerical solution of nonlinear weakly singular Volterra-Fredholm integral equations by using the product integration method. Also, we shall study the convergence behavior of a fully discrete version of a product integration method for numerical solution of the nonlinear Volterra-Fredholm integral equations. The reliability and efficiency of the proposed scheme are...

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, we use a combination of Legendre and Block-Pulse functionson the interval [0; 1] to solve the nonlinear integral equation of the second kind.The nonlinear part of the integral equation is approximated by Hybrid Legen-dre Block-Pulse functions, and the nonlinear integral equation is reduced to asystem of nonlinear equations. We give some numerical examples. To showapplicability of...

A nonlinear stochastic integral equation of the Hammerstein type in the form x(t; c) = h(t; co) + f k(t, s; co)f (s, x(s; co)) dy (s) is studied where t E S, a v-finite measure space with certain properties, co E Q, the supporting set of a probability measure space (Q, A, P), and the integral is a Bochner integral. A random solution of the equation is defined to be a second order vector-valued ...

An exponentially convergent approximation to the solution of a nonlinear first order differential equation with an operator coefficient in Banach space is proposed. The algorithm is based on an equivalent Volterra integral equation including the operator exponential generated by the operator coefficient. The operator exponential is represented by a Dunford-Cauchy integral along a hyperbola enve...

In this paper the fixed point theorem of Schauder is used to prove the existence of a continuous solution of the nonlinear fuzzy Volterra integral equations. Then using some conditions the uniqueness of the solution is investigated.

In this paper, a nonlinear inverse problem of parabolic type, is considered. By reducing this inverse problem to a system of Volterra integral equations the existence, uniqueness, and stability of the solution will be shown.