Construction of the solution of a homogeneous linear system of differential equations with constant coefficients by a matrix method

1977 ◽  
Vol 28 (6) ◽  
pp. 648-650
Author(s):  
Z. E. Filer
Keyword(s):  
Linear System ◽  
Differential Equations ◽  
Matrix Method ◽  
System Of Differential Equations ◽  
Constant Coefficients ◽  
Homogeneous Linear

scholarly journals Linear PDE with constant coefficients

2021 ◽  
pp. 1-26
Author(s):  
Rida Ait El Manssour ◽  
Marc Härkönen ◽  
Bernd Sturmfels
Keyword(s):  
Partial Differential Equations ◽  
Linear System ◽  
Differential Equations ◽  
Commutative Algebra ◽  
Fundamental Principle ◽  
Partial Differential ◽  
Linear Pde ◽  
Constant Coefficients ◽  
The 1960S ◽  
Homogeneous Linear

Abstract We discuss practical methods for computing the space of solutions to an arbitrary homogeneous linear system of partial differential equations with constant coefficients. These rest on the Fundamental Principle of Ehrenpreis–Palamodov from the 1960s. We develop this further using recent advances in computational commutative algebra.

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].

Sign in / Sign up

Export Citation Format

Share Document