in this paper‎, ‎we study the extremal‎ ‎ranks and inertias of the hermitian matrix expression $$‎ ‎f(x,y)=c_{4}-b_{4}y-(b_{4}y)^{*}-a_{4}xa_{4}^{*},$$ where $c_{4}$ is‎ ‎hermitian‎, ‎$*$ denotes the conjugate transpose‎, ‎$x$ and $y$ satisfy‎ ‎the following consistent system of matrix equations $a_{3}y=c_{3}‎, ‎a_{1}x=c_{1},xb_{1}=d_{1},a_{2}xa_{2}^{*}=c_{2},x=x^{*}.$ as‎ ‎consequences‎, ‎we g...

Differential–difference equation; Collocation points; Polynomial solutions Abstract This paper contributes a new matrix method for solving systems of high-order linear differential–difference equations with variable coefficients under given initial conditions. On the basis of the presented approach, the matrix forms of the Euler polynomials and their derivatives are constructed, and then by sub...

In this paper, the fuzzy matrix equation $Awidetilde{X}B=widetilde{C}$ in which $A,B$ are $n times n$crisp matrices respectively and $widetilde{C}$ is an $n times n$ arbitrary LR fuzzy numbers matrix, is investigated. A new numerical procedure for calculating the fuzzy solution is designed and a sufficient condition for the existence of strong fuzzy solution is derived. Some examples are ...

in this work, we proposed an efective method based on cubic and pantic b-spline scaling functions to solve partial differential equations of frac- tional order. our method is based on dual functions of b-spline scaling func- tions. we derived the operational matrix of fractional integration of cubic and pantic b-spline scaling functions and used them to transform the mentioned equations to a ...

this paper presents a new numerical method for solution of eikonal equation in two dimensions.in contrast to the previously developed methods which try to define the solution surface by its level sets(contour curves), the developed methodology identifies the solution surface by resorting to its characteristics. the suggested procedure is based on the geometric properties of the solution surface...

In this note we examine the solution and the impulsive behavior of autonomous linear multivariable systems whose pseudo-state β (t) obeys a linear matrix differential equation A (ρ)β (t) = 0 where A (ρ) is a polynomial matrix in the differential operator ρ := d dt . We thus generalize to the general polynomial matrix case some results obtained in [2][3] which regard the impulsive behavior of th...