Second-kind Volterra integral equations with weakly singular kernels typically have solutions which are nonsmooth near the initial point of the interval of integration. Using an adaptation of the analysis originally developed for nonlinear weakly singular Fredholm integral equations, we present a complete discussion of the optimal (global and local) order of convergence of piecewise polynomial ...

Keywords: Volterra integro-differential equations Multistep collocation Superconvergence Stability a b s t r a c t Multistep collocation methods for Volterra integro-differential equations are derived and analyzed. They increase the order of convergence of classical one-step collocation methods, at the same computational cost. The numerical stability analysis is carried out and classes of A 0-s...

This article aims at preferring a new and viable algorithm, specifically a two-step homotopy perturbation transform algorithm (TSHPTA). This novel technique is a feasible way in finding exact solutions with a small amount of calculations. As a simple but typical example, it demonstrates the strength and the great potential of the two-step homotopy perturbation transform method to solve nonlinea...

Recently, there has been an increasing interest in the study of singular and perturbed systems. In this paper we propose a collocation method for solving singularly perturbed Volterra integro-differential and Volterra integral equations. The method is based upon radial basis functions, using zeros of the shifted Legendre polynomial as the collocation points. The results of numerical experiments...

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...

In this paper, we continue our study that began in recent papers [2] and [3] concerning a simple yet effective Taylor series expansion method to approximate a solution of integral equations. The method is applied to Volterra integral equation of the second kind as well as to systems of Volterra equations. The results obtained in this paper improve significantly the results reported in recent pa...

This article introduces a numerical method based on an M(n+ 1) set of general, hybrid orthonormal Bernstein functions coupled with Block-Pulse Functions(HOBB) on the interval [0,1] for approximating solutions of a Coupled System of linear and non linear Volterra integral and Integro-Differential equations. This method reduces a Coupled System of Volterra integral and IntegroDifferential equatio...

Introduction: Power amplifiers (PAs) with high power efficiency are inherently nonlinear (NL). The requirements on linearity have increased since wideband signals with high peak-to-average ratios are used more in, e.g. mobile systems. Linearisation is, thus, necessary for high power efficiency of PAs. Digital predistortion (DPD) has attracted much interest since it is a cost-effective linearisa...

Starting from the Volterra approach and assuming fading memory, a very efficient method to identify weakly non-linear systems is presented. Making special assumptions on the Volterra kernels, one ends up in the Hammerstein model, which has less complexity than the Volterra model, thus reducing the numerical effort. Using FIR filters to realize the Hammerstein model, no starting values are neces...

In this article, by means of using discrete zero curvature representation and constructing opportune time evolution problems, two new discrete integrable lattice hierarchies with ndependent coefficients are proposed, which related to a new discrete Schrödinger nonisospectral operator equation. The relation of the two new lattice hierarchies with the Volterra hierarchy is discussed. It has been ...