this paper presents a comparison between variational iteration method (vim) and modfied variational iteration method (mvim) for approximate solution a system of volterra integral equation of the first kind. we convert a system of volterra integral equations to a system of volterra integro-di®erential equations that use vim and mvim to approximate solution of this system and hence obtain an appr...

Fuzzy logic is a soft computing technique that has been very successful in recent years when it is used as a complement to improve meta-heuristic optimization. In this paper, we present a new variant of the bio-inspired optimization algorithm based on the self-defense mechanisms of plants in the nature. The optimization algorithm proposed in this work is based on the predator-prey model origina...

In this paper we intend to offer new numerical methods to solve the fuzzy FredholmVolterra integral equations of the first kind (FV FIE − 1) base on collocation and Galerkin methods. Some examples are investigated to verify convergence results and to illustrate the efficiently of the methods.

Conventional Volterra series model is hardly applied to engineering practice due to its parametric complexity and estimation difficulty. To solve this problem, nonlinear system identification using reduced complexity Volterra models is proposed. Since the nonlinear components often play a secondary role compared to the dominant, linear component of the system, they spend the most of identificat...

This paper presents a comparison between variational iteration method (VIM) and modfied variational iteration method (MVIM) for approximate solution a system of Volterra integral equation of the first kind. We convert a system of Volterra integral equations to a system of Volterra integro-di®erential equations that use VIM and MVIM to approximate solution of this system and hence obtain an appr...

This is a short tutorial on Volterra and Wiener series applications to modelling of nonlinear systems and phenomena, and also a survey of the recent achievements in this area. In particular, we show here how the philosophies standing behind each of the above theories differ from each other. On the other hand, we discuss also mathematical relationships between Volterra and Wiener ker...

A parsimonious parameterization scheme is proposed to model the sparse Volterra filter so that the number of Volterra kernels to be estimated is greatly reduced. Representing the Volterra filter using a linear vector equation, the genetic algorithm is applied to search the significant terms among all possible candidate vectors. As the significant terms are detected, the associated Volterra kern...

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 ...

In this paper we intend to offer new numerical methods to solve the second-order fuzzy Abel-Volterraintegro-differential equations under the generalized $H$-differentiability. The existence and uniqueness of thesolution and convergence of the proposed methods are proved in details and the efficiency of the methods is illustrated through a numerical example.

In this study, differential transform method (DTM) is applied to fuzzy integro-differential equation. The concept of generalized Hdifferentiability is used. If the equation has a solution in terms of the series expansion of known functions; this powerful method catches the exact solution. Some numerical examples are also given to illustrate the superiority of the method. All rights reserved.