scholarly journals An Alternative Algorithm for the Symmetry Classification of Ordinary Differential Equations

2022 ◽  
Vol 56 (1) ◽  
pp. 65-76
Author(s):  
Yi Tian ◽  
Jing Pang
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Symmetry Classification ◽  
Alternative Algorithm

scholarly journals Approximate transformations for van der Pol-type equations

2006 ◽  
Vol 2006 ◽  
pp. 1-11 ◽  
Author(s):  
R. K. Gazizov ◽  
C. M. Khalique
Keyword(s):  
Differential Equations ◽  
Small Parameter ◽  
Ordinary Differential Equations ◽  
Transformation Groups ◽  
Van Der Pol ◽  
Approximate Symmetries ◽  
Approximate Integration ◽  
Successive Reduction

Classification of van der Pol-type equations with respect to admitted approximate transformation groups transforming a small parameter is given. It is shown that approximate symmetries transforming the small parameter as well as the usual approximate symmetries can be used for approximate integration (e.g., by method of successive reduction of order) of ordinary differential equations with a small parameter.

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