In this paper we study a class of quadratic operators named by Volterra operators on infinite dimensional space. We prove that such operators have infinitely many fixed points and the set of Volterra operators forms a convex compact set. In addition, it is described its extreme points. Besides, we study certain limit behaviors of such operators and give some more examples of Volterra operators ...

We give a construction of a cubic stochastic operator (CSO) on a finite dimensional simplex. This construction depends on a probability measure μ which is given on a fixed finite graph G. Using the construction of CSO for μ defined as product of measures given on components of G a wide class of non-Volterra CSOs is described. It is shown that the non-Volterra operators can be reduced to N numbe...

In this paper, a numerical efficient method based on two-dimensional block-pulse functions (BPFs) is proposed to approximate a solution of the two-dimensional linear stochastic Volterra-Fredholm integral equation. Finally the accuracy of this method will be shown by an example.

in this paper we consider a nonlinear two-phase stefan problem in one-dimensional space. the problem is mapped into a nonlinear volterra integral equation for the free boundary.

in this paper, the two-dimensional triangular orthogonal functions (2d-tfs) are applied for solving a class of nonlinear two-dimensional volterra integral equations. 2d-tfs method transforms these integral equations into a system of linear algebraic equations. the high accuracy of this method is verified through a numerical example and comparison of the results with the other numerical methods.

Hirota’s bilinear technique is applied to some integrable lattice systems related to the Bäcklund transformations of the 2DToda, Lotka-Volterra and relativistic LotkaVolterra lattice systems, which include the modified Lotka-Volterra lattice system, the modified relativistic Lotka-Volterra lattice system, and the generalized BlaszakMarciniak lattice systems. Determinant solutions are constructe...

In this paper, we study the approximate solution of two-dimensional nonlinear Volterra integral equations by two-dimensional differential transform method. New theorems for the transformation of integrals are introduced and proved. We will give an applicable relation between the two-dimensional nonlinear Volterra integral equations and two-dimensional differential transformation, in order to so...

In this paper, the two-dimensional triangular orthogonal functions (2D-TFs) are applied for solving a class of nonlinear two-dimensional Volterra integral equations. 2D-TFs method transforms these integral equations into a system of linear algebraic equations. The high accuracy of this method is verified through a numerical example and comparison of the results with the other numerical methods.

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...

The response of visual cells is a nonlinear function of their stimuli. In addition, an increasing amount of evidence shows that visual cells are optimized to process natural images. Hence, finding good nonlinear models to characterize visual cells using natural stimuli is important. The Volterra model is an appealing nonlinear model for visual cells. However, their large number of parameters an...