Correlation functions of exactly solvable models can be described by differential equations [1]. In this paper we show that for non free fermionic case differential equations should be replaced by integro-differential equations. We derive an integro-differential equation, which describes time and temperature dependent correlation function 〈ψ(0, 0)ψ(x, t)〉T of penetrable Bose gas. The integrodif...

In this paper, we present a Taylor-series expansion method for a class of Fredholm singular integro-differential equation with Cauchy kernel. This method uses the truncated Taylor-series polynomial of the unknown function and transforms the integro-differential equation into an nth order linear ordinary differential equa.tion with variable coefficients: ~y Galerkin method we use the orthogonal ...

This work studies various types of input/output representations for analytic input/output operators. It is shown that if an operator satisfies an integro-differential input/output equation or an integral one, then it is locally realizable by analytic state space systems. This generalizes the results previously obtained for differential input/output equations to integral and integro-differential...

In this paper, by using the theories and methods of integral equation and computer algebra, a reliable algorithm for solving the Volterra integral equation is established, and a new Maple algorithm mainproc is established, too. Some examples are presented to illustrate the implementations of the algorithm. The results of the examples indicate that the algorithm of Taylor polynomial method is si...

Abstract This paper presents an appropriate numerical method to solve nonlinear Fredholm integro-differential equations with time delay. Its approach is based on the Taylor expansion. This method converts the integro-differential equation and the given conditions into the matrix equation which corresponds to a system of nonlinear algebraic equations with unknown Taylor expansion coefficients, s...

In this paper, we propose a method to approximate the solution of a linear Fredholm integro-differential equation by using the Chebyshev wavelet of the first kind as basis. For this purpose, we introduce the first Chebyshev operational matrix of integration. Chebyshev wavelet approximating method is then utilized to reduce the integro-differential equation to a system of algebraic equations. Il...

In this article we have considered Fredholm integro-differential equation type second-order boundary value problems and proposed a rational difference method for numerical solution of the problems. The composite trapezoidal quadrature and non-standard difference method are used to convert Fredholm integro-differential equation into a system of equations. The numerical results in experiment on s...

The homotopy analysis method [1, 2], is developed to search the accurate asymptotic solutions of nonlinear problems. This technique has been successfully applied to many nonlinear problems such as the viscous flows of non-Newtonian fluids [3, 4], the Korteweg-de Vries-type equations [5, 6], nonlinear heat transfer [7, 8], finance problems [9, 10], Riemann problems related to nonlinear shallow w...

Coarsening of solutions of the integro-differential equation