In this paper, an effective numerical method is introduced for the treatment of nonlinear two-dimensional Volterra-Fredholm integro-differential equations. Here, we use the so-called two-dimensional block-pulse functions.First, the two-dimensional block-pulse operational matrix of integration and differentiation has been presented. Then, by using this matrices, the nonlinear two-dimensional Vol...

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, Adomian decomposition method (ADM) and homotopy analysis method (HAM) are proposed to solving the fuzzy nonlinear Volterra-Fredholm integral equation of the second kind(FV FIE− 2). we convert a fuzzy nonlinear Volterra-Fredholm integral equation to a nonlinear system of Volterra-Fredholm integral equation in crisp case. we use ADM , HAM and find the approximate solution of this s...

*Correspondence: [email protected] School of Mathematics and Physics, Changzhou University, Changzhou, Jiangsu 213164, China Abstract In this paper, we provide a new approach for discussing the solvability of a class of operator equations by establishing fixed point theorems in locally convex spaces. Our results are obtained extend some Krasnosel’skii type fixed point theorems. As an applicatio...

Nonlinear adaptive filtering techniques, based on the Volterra model, are widely used for the nonlinearities identification in many applications. This paper proposes a new implementation of the third order LMS Volterra filter. A third order nonlinear system with memory is identified using the new LMS algorithm implementation for the Volterra kernels estimation. The accuracy of the proposed algo...

Abstract A new numerical method based on Haar wavelet is proposed for two-dimensional nonlinear Fredholm, Volterra and Volterra-Fredholm integral equations of first and second kind. The proposed method is an extension of the Haar wavelet method [1–3] from one-dimensional nonlinear integral equations (Fredholm and Volterra) to twodimensional nonlinear integral equations (Fredholm, Volterra and V...

This paper presents a numerical matrix method based on Bernstein polynomials (BPs) for approximate the solution of a system of m-th order nonlinear Volterra integro-differential equations under initial conditions. The approach is based on operational matrices of BPs. Using the collocation points,this approach reduces the systems of Volterra integro-differential equations associated with the giv...

In this work, the existence and uniqueness solution of fractional nonlinear mixed integro-differential equation (FrNMIoDE) is guaranteed with a general discontinuous kernel based on position time-space L2Ω×C0,T, T<1. The FrNMIoDE conformed to Volterra-Hammerstein integral (V-HIE) second kind, after applying characteristics integral, in for Hammerstein term continuous time Volterra (VI) term....

Volterra series is a powerful tool for blackbox macromodeling of nonlinear devices. However, the exponential complexity growth in storing and evaluating higher order Volterra kernels has limited so far its employment on complex practical applications. On the other hand, tensors are a higher order generalization of matrices that can naturally and efficiently capture multidimensional data. Signif...

In this paper, we propose and analyze an efficient matrix method based on Bell polynomials for numerically solving nonlinear Fredholm- Volterra integral equations. For this aim, first we calculate operational matrix of integration and product based on Bell polynomials. By using these matrices, nonlinear Fredholm-Volterra integral equations reduce to the system of nonlinear algebraic equations w...