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Algorithm for solution of systems of singularly perturbed differential equations with adifferential turning point

Sobchuk Valentyn, Zelenska Iryna, Laptiev Oleksandr

Bulletin of the Polish Academy of Sciences. Technical Sciences

2023

Vol. 71, nr 3

art. no. e145682

The dynamic development of science requires constant improvement of approaches to modeling physical processes and phenomena. Practically all scientific problems can be described by systems of differential equations. Many scientific problems are described by systems of differential equations of a special class, which belong to the group of so-called singularly perturbed differential equations. Mathematical models of processes described by such differential equations contain a small parameter near the highest derivatives, and it was the presence of this small factor that led to the creation of a large mathematical theory. The work proposes a developed algorithm for constructing uniform asymptotics of solutions to systems of singularly perturbed differential equations.

Anoccupational measure solution to a singularly perturbed optimal control problem

Artstein Z.

Control and Cybernetics

2002

Vol. 31, no 3

623-642

Employing limit occupational measures, we provide an explicit solution to a singularly perturbed optimal control problem for which the order reduction method does not apply.