Symmetries and first order ODE patterns

A scheme for determining symmetries for certain families of first order ODEs, without solving any differential equations, and based mainly in matching an ODE to patterns of invariant ODE families, is presented. The scheme was implemented in Maple, in the framework of the ODEtools package and its ODE...

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Bibliographic Details
Published in:Computer physics communications 1998-10, Vol.113 (2-3), p.239-260
Main Authors: Cheb-Terrab, E.S., Roche, A.D.
Format: Article
Language:English
Subjects:
Exact sciences and technology
First order ordinary differential equations
Function theory, analysis
Mathematical methods in physics
Ordinary differential equations
Physics
Symbolic computation
Symmetry methods
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Summary:A scheme for determining symmetries for certain families of first order ODEs, without solving any differential equations, and based mainly in matching an ODE to patterns of invariant ODE families, is presented. The scheme was implemented in Maple, in the framework of the ODEtools package and its ODE-solver. A statistics of the performance of this approach in solving the first order ODE examples of Kamke's book (E. Kamke, Differentialgleichungen: Lösungsmethoden und Lösungen (Chelsea, New York, 1959)) is shown.
ISSN:0010-4655
1879-2944
DOI:10.1016/S0010-4655(98)00071-X