In this letter, the numerical scheme of nonlinear Volterra-Fredholm integro-differential equations is proposed in a reproducing kernel Hilbert space (RKHS). The method is constructed based on the reproducing kernel properties in which the initial condition of the problem is satised. The nonlinear terms are replaced by its Taylor series. In this technique, the nonlinear Volterra-Fredholm integro...

In this paper, we propose a low complexity realization method for compensating for nonlinear distortion. Generally, nonlinear distortion is compensated for by a linearization system using a Volterra kernel. However, this method has a problem of requiring a huge computational complexity for the convolution needed between an input signal and the 2nd-order Volterra kernel. The Simplified Volterra ...

In this paper, to solve a linear one-dimensional Volterra  integral equation of the second kind. For this purpose using the equation form, we have defined a linear transformation and by using it's conjugate and reproducing kernel functions, we obtain a basis for the functions space.Then we obtain the solution of  integral equation in terms of the basis functions. The examples presented in this ...

Aiming at the nonlinear filtering problem that exists when the input and output observation data are both corrupted by noises, a stable total least square adaptive algorithm for the nonlinear Volterra filter is proposed in this paper. Taking the minimum Rayleigh Quotient of the augmented Volterra weight vectors and a constraint to the last element of the augmented Volterra weight vectors via a ...

In this paper, a nonlinear acoustic echo cancellation (AEC) system is proposed, whereby 3rd order Volterra filtering is utilized along with a variable step-size Gauss-Seidel pseudo affine projection (VSSGS-PAP) algorithm. In particular, the proposed nonlinear AEC system is developed by considering a double-talk situation with near-end signal variation. Simulation results demonstrate that the pr...

Nonlinear intersymbol interferences (ISI) often arise in voiceThe major drawback of the Volterra approach is the enormous band communication channels at high transmission rates or in complexity. Even when the symmetry in the 3rd order Volterra satellite channels due to nonlinearities in the power amplifiers. Proposed equalizers for the cancellation of these nonlinear interferences are mainly ba...

This dissertation is primarily concerned with the estimation of nonlinear communication systems that are modeled by Volterra series. The major methods used for estimating the unknown channel parameters can be classified into two main categories: training-based and blind. First, orthobasis representation and training-based identification through the respective Fourier series are investigated for...

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, 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...