in this paper, some basic results concerning strict, nonstrict inequalities, local existence theorem and differential inequalities  have been proved for an ivp of first order hybrid  random differential equations with the linear perturbation of second type. a comparison theorem is proved and  applied to prove the uniqueness of random solution for the considered perturbed random differential equ...

in this paper, we propose a new method for solving the stochastic advection-diffusion equation of ito type. in this work, we use a compact finite difference approximation for discretizing spatial derivatives of the mentioned equation and semi-implicit milstein scheme for the resulting linear stochastic system of differential equation. the main purpose of this paper is the stability investigatio...

Using the operational matrix of an orthogonal function to perform integration for solving, identifying and optimizing a linear dynamic system has several advantages: (1) the method is computer oriented, thus solving higher order differential equation becomes a matter of dimension increasing; (2) the solution is a multiresolution type; (3) the answer is convergent, even the size of increment is ...

Universit .2012.07.0 Abstract A Taylor collocation method has been developed to solve the systems of high-order linear differential–difference equations in terms of the Taylor polynomials. Using the Taylor collocation points, this method transforms differential–difference equation systems and the given conditions to matrix equations with unknown Taylor coefficients. By means of the obtained mat...

A q-difference analog of the sixth Painlevé equation is presented. It arises as the condition for preserving the connection matrix of linear q-difference equations, in close analogy with the monodromy preserving deformation of linear differential equations. The continuous limit and special solutions in terms of q-hypergeometric functions are also discussed.

Descriptor systems consisting of a large number of differential-algebraic equations (DAEs) usually arise from the discretization of partial differential-algebraic equations. This paper presents an efficient algorithm for solving the coupled Sylvester equation that arises in converting a system of linear DAEs to ordinary differential equations. A significant computational advantage is obtained b...

We study the Galois group of a matrix q-difference equation with rational coefficients which is regular at 0 and ∞, in the sense of (difference) Picard-Vessiot theory, and show that it coincides with the algebraic group generated by matrices C(u)C(w)−1 u,w ∈ C∗ , where C(z) is the Birkhoff connection matrix of the equation. 1. Differential algebra The notion of the Galois group of a linear ordi...

430 NOTICES OF THE AMS VOLUME 49, NUMBER 4 Linear Ordinary Differential Equations How to solve linear ordinary differential equations? Like many outstanding mysteries of mathematics, this question has the virtue of simplicity. Linear differential equations are the staple of every mathematical syllabus, familiar to all and sundry, and their investigation has informed much of the development of m...