On rational function approximations to the exponential function with application to the practical solution of linear differential difference equations with constant coefficients

1956 ◽  
Author(s):  
Yudell L. Luke
Keyword(s):  
Rational Function ◽  
Exponential Function ◽  
Difference Equations ◽  
Practical Solution ◽  
Constant Coefficients ◽  
Linear Differential ◽  
Function Approximations

A modified Lorenz system: Definition and solution

2020 ◽  
Vol 13 (08) ◽  
pp. 2050164
Author(s):  
Biljana Zlatanovska ◽  
Donc̆o Dimovski
Keyword(s):  
Differential Equations ◽  
Difference Equations ◽  
Lorenz System ◽  
Local Approximation ◽  
System Of Differential Equations ◽  
Lorentz System ◽  
Constant Coefficients ◽  
Linear Differential ◽  
The Lorenz System ◽  
Fifth Order

Based on the approximations of the Lorenz system of differential equations from the papers [B. Zlatanovska and D. Dimovski, Systems of difference equations approximating the Lorentz system of differential equations, Contributions Sec. Math. Tech. Sci. Manu. XXXIII 1–2 (2012) 75–96, B. Zlatanovska and D. Dimovski, Systems of difference equations as a model for the Lorentz system, in Proc. 5th Int. Scientific Conf. FMNS, Vol. I (Blagoevgrad, Bulgaria, 2013), pp. 102–107, B. Zlatanovska, Approximation for the solutions of Lorenz system with systems of differential equations, Bull. Math. 41(1) (2017) 51–61], we define a Modified Lorenz system, that is a local approximation of the Lorenz system. It is a system of three differential equations, the first two are the same as the first two of the Lorenz system, and the third one is a homogeneous linear differential equation of fifth order with constant coefficients. The solution of this system is based on the results from [D. Dimitrovski and M. Mijatovic, A New Approach to the Theory of Ordinary Differential Equations (Numerus, Skopje, 1995), pp. 23–33].

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.

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