SUR UNE CLASSIFICATION TOPOLOGIQUE DES SYSTÈMES DIFFÉRENTIELS - KEHALI Salima (University of M'Sila, 2024)
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.
Keywords: differential equation systems; integral equations; collocation method; Hermite polynomials