In this second part of paper the description of conservative averaging method for partial differential (or integro-differential) equation with discontinuous coefficients in cylinder type domain is given. The conservative averaging is carried out in two orthogonal directions. Different types of boundary conditions are examined. Key-Words: partial differential equations, discontinuous coefficient...

Due to the plentiful dynamical behaviors, integro-differential equations with delays have many applications in a variety of fields such as control theory, biology, ecology, medicine, etc [1, 2]. Especially, the effects of delays on the stability of integro-differential equations have been extensively studied in the previous literature (see [3]-[9] and references cited therein). Besides delays, ...

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...

A two-person pursuit-evasion stochastic differential game with state and measurement,y corrupted by noises is considered. In an earlier paper the problem was reformulated and solved in an infinite-dimensional-state space, and the existence of saddle-point solutions under certain conditions was proved. 7he present paper provides a numerical solution for the resulting continuous-time integro-part...

In this paper, we study a class of impulsive neutral stochastic functional integro-differential equations with infinite delay driven by a standard cylindrical Wiener process and an independent cylindrical fractional Brownian motion (fBm) with Hurst parameter H 2 ð1=2; 1Þ in the Hilbert space. We prove the existence and uniqueness of the mild solution for this kind of equations with the coeffici...

Abstract: This article focuses on obtaining analytical solutions for d-dimensional, parabolic Volterra integro-differential equations with different types of frictional memory kernel. Based on Laplace transform and Fourier transform theories, the properties of the Fox-H function and convolution theorem, analytical solutions for the equations in the infinite domain are derived under three fricti...

This paper is concerned with obtaining the approximate solution of Fredholm-Volterra integro-differential equations. Properties of the Shannon wavelets and connection coefficients are first presented. We design a numerical scheme for these equations using the Galerkin method incorporated with the Shannon wavelets approximation and the connection coefficients. We will show that using this techni...

We review our algebraic framework for linear boundary problems (concentrating on ordinary differential equations). Its starting point is an appropriate algebraization of the domain of functions, which we have named integro-differential algebras. The algebraic treatment of boundary problems brings up two new algebraic structures whose symbolic representation and computational realization is base...

The notion of integro-differential algebra was introduced in [Rosenkranz, M. and Regensburger, G.: Solving and Factoring Boundary Problems for Linear Ordinary Differential Equations in Differential Algebras, J. Symbolic Comput., 2008(43/8), pp. 515–544] to facilitate the algebraic study of boundary problems for linear ordinary differential equations. In this report, we construct a discrete anal...