scholarly journals On two-sided solutions of a linear system with asymptotically constant coefficients and delay

1983 ◽  
Vol 33 (1) ◽  
pp. 58-69
Author(s):  
S. B. Norkin
Keyword(s):  
Linear System ◽  
Constant Coefficients

scholarly journals Differential transcendence of solutions of systems of linear differential equations based on total reduction of the system

2020 ◽  
pp. 24-24
Author(s):  
Ivana Jovovic
Keyword(s):  
Linear System ◽  
Differential Equations ◽  
Complex Field ◽  
System Matrix ◽  
Operator Equations ◽  
Total Reduction ◽  
Commuting Operators ◽  
Constant Coefficients ◽  
Linear Differential ◽  
System Of Operator Equations

In this paper we consider total reduction of the nonhomogeneous linear system of operator equations with constant coefficients and commuting operators. The totally reduced system obtained in this manner is completely decoupled. All equations of the system differ only in the variables and in the nonhomogeneous terms. The homogeneous parts are obtained using the generalized characteristic polynomial of the system matrix. We also indicate how this technique may be used to examine differential transcendence of the solution of the linear system of the differential equations with constant coefficients over the complex field and meromorphic free terms.

scholarly journals Linearization of Two Second-Order Ordinary Differential Equations via Fiber Preserving Point Transformations

2011 ◽  
Vol 2011 ◽  
pp. 1-21 ◽  
Author(s):  
Sakka Sookmee ◽  
Sergey V. Meleshko
Keyword(s):  
Linear System ◽  
General Solution ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Necessary Conditions ◽  
Second Order ◽  
Point Transformations ◽  
Constant Coefficients ◽  
Linearizable System

The necessary form of a linearizable system of two second-order ordinary differential equations y1″=f1(x,y1,y2,y1′,y2′), y2″=f2(x,y1,y2,y1′,y2′) is obtained. Some other necessary conditions were also found. The main problem studied in the paper is to obtain criteria for a system to be equivalent to a linear system with constant coefficients under fiber preserving transformations. A linear system with constant coefficients is chosen because of its simplicity in finding the general solution. Examples demonstrating the procedure of using the linearization theorems are presented.

scholarly journals Differential Transcendency in the Theory of Linear Differential Systems with Constant Coefficients

2012 ◽  
Vol 2012 ◽  
pp. 1-8
Author(s):  
Branko Malešević ◽  
Dragana Todorić ◽  
Ivana Jovović ◽  
Sonja Telebaković
Keyword(s):  
Cauchy Problem ◽  
Linear System ◽  
Order Operator ◽  
Operator Equations ◽  
Differential Systems ◽  
First Order ◽  
Linear Differential Systems ◽  
Constant Coefficients ◽  
Linear Differential

We consider a reduction of a nonhomogeneous linear system of first-order operator equations to a totally reduced system. Obtained results are applied to Cauchy problem for linear differential systems with constant coefficients and to the question of differential transcendency.

scholarly journals Conditions for Factorization of Linear Differential-Difference Equations

2013 ◽  
Vol 54 (1) ◽  
pp. 93-99
Author(s):  
Klara R. Janglajew ◽  
Kim G. Valeev
Keyword(s):  
Linear System ◽  
Small Parameter ◽  
Difference Equations ◽  
Integral Manifold ◽  
Sufficient Conditions ◽  
System Of Differential Equations ◽  
Deviating Argument ◽  
Constant Coefficients ◽  
Complex Deviating Argument ◽  
Linear Differential

Abstract The paper deals with a linear system of differential equations of the form with constant coefficients, a small parameter and complex deviating argument. Sufficient conditions for factorizing of this system are presented. These conditions are obtained by construction of an integral manifold of solutions to the considered system.

scholarly journals Symbolic Solution to Complete Ordinary Differential Equations with Constant Coefficients

2013 ◽  
Vol 2013 ◽  
pp. 1-15
Author(s):  
Juan F. Navarro ◽  
Antonio Pérez-Carrió
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Exact Solution ◽  
Linear System ◽  
Differential Equations ◽  
Test Problem ◽  
Homogeneous Equation ◽  
Variation Of Parameters ◽  
Constant Coefficients ◽  
Exponential Matrix

The aim of this paper is to introduce a symbolic technique for the computation of the solution to a complete ordinary differential equation with constant coefficients. The symbolic solution is computed via the variation of parameters method and, thus, constructed over the exponential matrix of the linear system associated with the homogeneous equation. This matrix is also symbolically determined. The accuracy of the symbolic solution is tested by comparing it with the exact solution of a test problem.

Sign in / Sign up

Export Citation Format

Share Document