This article proposes an optimal method for approximate answer of stochastic Ito-Voltrra integral equations, via rationalized Haar functions and their stochastic operational matrix of integration. Stochastic Ito-voltreea integral equation is reduced to a system of linear equations. This scheme is applied for some examples. The results show the efficiency and accuracy of the method.

abstract. the main contribution of the current paper is to propose a new effective numerical method for solving the first-order linear matrix differential equations. properties of the legendre basis operational matrix of integration together with a collocation method are applied to reduce the problem to a coupled linear matrix equations. afterwards, an iterative algorithm is examined for solvin...

Let Rn,d be the ring of invariants of d-tuples of n × n matrices under the simultaneous conjugation action of the general linear group. A minimal generating system and a homogeneous system of parameters of R3,3 are determined. Homogeneous systems of parameters of R3,2, R4,2 are also pointed out.

This paper examines finite-time stability of homogeneous systems. The main result is that a homogeneous system is finite-time stable if and only if it is asymptotically stable and has a negative degree of homogeneity.

In this work, we will prove the Hyers–Ulam stability of linear partial differential equations of first order.