SUR UNE CLASSIFICATION TOPOLOGIQUE DES SYSTÈMES DIFFÉRENTIELS
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Date
2024-02-26
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University of M'Sila
Abstract
The objective of this work is to study the topology of systems of linear and nonlinear
differential equations of the following form:
1 1 1 2
2 2 1 2
1 2
'( ) ( , ( ), ( ),... ( ))
'( ) ( , ( ), ( ),... ( ))
'( ) ( , ( ), ( ),... ( ))
n
n
n n n
v s L s v s v s v s
v s L s v s v s v s
v s L s v s v s v s
We have adopted the Lyapunov stability criterion for the differential system. Following this,
we explored the numerical study by leveraging the relationship between differential systems
and integral equations, passing through differential equations. For each example, we
transformed a differential system into a differential equation, and then into an equivalent
integral equation, ultimately deriving an approximate solution using the collocation method
and Hermite polynomials. Promising results were achieved.
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Keywords
differential equation systems, integral equations, collocation method, Hermite polynomials