We investigate the structure of the nonlocal closure relation in the kinetic equation for a soliton gas. This kinetic equation represents an integro-differential nonlinear system which has been recently shown to possess a number of remarkable properties and seems to be a representative of an entirely new class of integrable systems. In this paper, we identify the nonlocal kinetic closure relati...

in this paper, the variational iteration method for solving nth-order fuzzy integro differential equations (nth-fide) is proposed. in fact the problem is changed to the system of ordinary fuzzy integro-differential equations and then fuzzy solution of nth-fide is obtained. some examples show the efficiency of the proposed method.

Abstract This paper discusses different types of Ulam stability first-order nonlinear Volterra delay integro-differential equations with impulses. Such allow the presence two kinds memory effects represented by and kernel used fractional integral operator. Our analysis is based on Pachpatte’s inequality fixed point approach Picard operators. Applications are provided to illustrate results obtai...

The main purpose of this study is to investigate solutions some integral equations different classes using a new scheme. This research introduces and implements the double ARA transform solve partial integro-differential equations. We introduce basic theorems properties in two dimensions, results related convolution theorem derivatives are presented. In addition, show validity proposed techniqu...

The paper considers two types of Volterra integral equations the first kind, arising in study inverse problems dynamics controlled heat power systems. main focus work is aimed at studying specifics classes kind that arise when describing nonlinear using apparatus integro-power series. subject area research represented by a simulation model exchange unit element, which describes change enthalpy ...

This paper presents a new technique for numerical treatments of Volterra delay integro-differential equations that have many applications in biological and physical sciences. The technique is based on the mono-implicit Runge — Kutta method (described in [12]) for treating the differential part and the collocation method (using Boole’s quadrature rule) for treating the integral part. The efficie...

Most boundary element methods for two-dimensional boundary value problems are based on point collocation on the boundary and the use of splines as trial functions. Here we present a unified asymptotic error analysis for even as well as for odd degree splines subordinate to uniform or smoothly graded meshes and prove asymptotic convergence of optimal order. The equations are collocated at the br...

By making use of asymptotic properties of nonoscillatory solutions the oscillation behavior of solutions for the integro-dynamic equation x(t) = e(t) − ∫ t 0 k(t, s)f(s, x(s))∆s, t ≥ 0 and the integral equation x(t) = e(t) − ∫ t 0 k(t, s)f(s, x(s))∆s, t ≥ 0 on time-scales are investigated. Easily verifiable sufficient conditions are established for the oscillation of all solutions. The results ...

Abstract. This paper is concerned with a model system for radiation hydrodynamics in multiple space dimensions. The system depends singularly on the light speed c and consists of a scalar nonlinear balance law coupled via an integral-type source term to a family of radiation transport equations. We first show existence of entropy solutions to Cauchy problems of the model system in the framework...

Abstract In this paper we consider a numerical scheme for the treatment of an integro-differential equation. The latter represents formulation nonlocal diffusion type discretization procedure relies on application line method. However, quadrature formulae are needed evaluation integral operator. They based generalized Bernstein polynomials. Numerical evidence shows that proposed method is suita...