This paper is concerned with a technique for solving Volterra integral equations in the reproducing kernel Hilbert space. In contrast with the conventional reproducing kernel method,the Gram-Schmidt process is omitted here and satisfactory results are obtained. The analytical solution is represented in the form of series. An iterative method is given to obtain the approximate solution. The conv...

We study the control systems governed by abstract Volterra equations without uniqueness in a Banach space. By using the technique of the theory of condensing maps and multivalued analysis tools, we obtain the existence result, investigate the topological structure of the solution set, and prove the invariance of a reachability set of the control system under nonlinear perturbations. Examples co...

In this study, we use Whittaker cardinal expansion and collocation method to approximate the solution of Volterra integral equation of the second kind numerically which is arisen in many mathematical, industrial and medical problems. Then convergence of this method will be discussed in L space for every positive . At the end of the paper, some numerical examples are presented to guarantee the a...

Abstract. The procedure of solving the system of the Navier-Stokes equations is proposed. The initial conditions: the velocity divergence (dilatation) being zero and the temperature being the known function, the initial density being constant. The problem is set in the infinite space. The solution of the Navier-Stokes equations was reduced to the solution of integral equations of the Volterra t...

The Volterra series can be used to model a large subset of nonlinear, dynamic systems. A major drawback is the number of coefficients required model such systems. In order to reduce the number of required coefficients, Laguerre polynomials are used to estimate the Volterra kernels. Existing literature proposes algorithms for a fixed number of Volterra kernels, and Laguerre series. This paper pr...

This paper mainly studied the LMS adaptive filter algorithm to the Volterra system model. Through the construction of the second order Volterra system model, the application of respectively selecting the first order and second order variable step length de-correlation Volterra LMS algorithm in gaussian noise environment, when the input signals in different correlation coefficient, the iteration...

In this article, by means of considering an isospectral operator equation which corresponds to the Volterra lattice, and constructing opportune time evolution problems with negative powers of spectral parameter, and using discrete zero curvature representation, negative Volterra flows are proposed. We also propose the mixed Volterra flows, which come from positive and negative volterra flows. F...

Discrete-time Volterra models play an important role in many application areas. The main drawback of these models is their parametric complexity due to the huge number of their parameters, the kernel coefficients. Using the symmetry property of the Volterra kernels, these ones can be viewed as symmetric tensors. In this paper, we apply tensor decompositions (PARAFAC and HOSVD) for reducing the ...

In the present paper we introduce a notion of homotopy of two Volterra operators which is related to fixed points of such operators. It is establish a criterion when two Volterra operators are homotopic, as a consequence we obtain that the corresponding tournaments of that operators are the same. This, due to [4], gives us a possibility to know some information about the trajectory of homotopic...