scholarly journals Symbolic Implementation of Preliminary Group Classiffication for Ordinary Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
K. S. Govinder
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Group Classification ◽  
Symmetry Analysis ◽  
Analysis Package ◽  
Small File ◽  
Fowler Equation ◽  
Preliminary Group

We apply the method of preliminary group classification to ordinary differential equations of the formy(n)=E(x,y,y',…,y(n-1),fi(x)),  i=0,…,m.We show how this method can be implemented via the popular symmetry analysis packagePROGRAM LIEprovided that the package is supplemented with a small file. We then apply this method to an extension of the generalised Emden-Fowler equation given byy′′=∑i=25fixyi.

scholarly journals GROUP PROPERTIES OF A ONE-DIMENSIONAL NONLINEAR POROELASTICITY EQUATION

2019 ◽  
Vol 4 (1) ◽  
pp. 149-155
Author(s):  
Kholmatzhon Imomnazarov ◽  
Ravshanbek Yusupov ◽  
Ilham Iskandarov
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Lie Algebra ◽  
Three Dimensional ◽  
Group Classification ◽  
Second Order ◽  
Partial Differential ◽  
One Dimensional ◽  
Preliminary Group

This paper studies a class of partial differential equations of second order , with arbitrary functions and , with the help of the group classification. The main Lie algebra of infinitely infinitesimal symmetries is three-dimensional. We use the method of preliminary group classification for obtaining the classifications of these equations for a one-dimensional extension of the main Lie algebra.

scholarly journals Lie group classification of first-order delay ordinary differential equations

2018 ◽  
Vol 51 (20) ◽  
pp. 205202 ◽  
Author(s):  
Vladimir A Dorodnitsyn ◽  
Roman Kozlov ◽  
Sergey V Meleshko ◽  
Pavel Winternitz
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Lie Group ◽  
Group Classification ◽  
First Order ◽  
Lie Group Classification
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