In this paper, we develop and modify Taylor-series expansion method to approximate a solution of nonlinear Volterra integro-differential equations (IDEs) as well as a solution of a system of nonlinear Volterra equations. By means of the nth-order Taylor-series expansion of an unknown function at an arbitrary point, a nonlinear Volterra equations can be converted approximately to a system of non...

The main purpose of this work is to provide a novel numerical approach for the Volterra integral equations based on a spectral approach. A Legendre-collocation method is proposed to solve the Volterra integral equations of the second kind. We provide a rigorous error analysis for the proposed method, which indicate that the numerical errors (in the infinity norm) will decay exponentially provid...

This paper, first, we consider the Volterra integral equation for remainder term in asymptotic formula associated Euler totient function. Secondly, solve and split error function into two summands called arithmetic analytic part respectively.

We discuss the notion of Volterra, l-Volterra and separable quadratic stochastic operators defined on (m− 1)-dimensional simplex, where l ∈ {0, 1, ...,m}. The l-Volterra operator is a Volterra operator if and only if l = m. We study the structure of the set of all Volterra and l-Volterra operators and describe their several fixed and periodic points. For m = 2 and m = 3 we describe behavior of ...

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...

We consider nonlinear, probability measure{valued dynamical systems that generalise those classical Lotka{Volterra equations in which, to use ecological terminology, the total size of a nite number of populations of interacting species is conserved. In our generalisation there is a \di erent species" at each point of an arbitrary measurable space. Such in nitely{many{species analogues of the cl...

‎ in this paper, we investigate stability analysis of fractional differential systems equipped with the conformable fractional derivatives. some stability conditions of fractional differential systems are proposed by applying the fractional exponential function and the fractional laplace transform. moreover, we check the stability of conformable fractional lotka-volterra system with the multi-st...

Dynamical behaviors of the competitive Lotka-Volterra system even for 3 species are not fully understood. In this paper, we study this problem from the perspective of the Lyapunov function. We construct explicitly the Lyapunov function using three examples of the competitive Lotka-Volterra system for the whole state space: (1) the general 2-species case, (2) a 3-species model, and (3) the model...

stefan problem with kinetics is reduced to a system of nonlinear volterra integral equations of second kind and newton's method is applied to linearize it. product integration solution of the linear form is found and sufficient conditions for convergence of the numerical method are given. an example is provided to illustrated the applicability of the method.

Algebraic integral equations is a special category of Volterra integral equations system,  that has many applications in physics and engineering. The principal aim of this paper is to serve the numerical solution of an integral algebraic equation by using the Taylor expansion method. In this method, using the Taylor expansion of the unknown function, the algebraic integral equation system becom...