Piece-wise smooth differential equations (their regularization, numerical integration, and classification of solutions) is the topic of the present work. The behaviour close to one discontinuity surface and also the entering into the intersection of two discontinuity surfaces is well understood. Here, we study the solutions that exit a codimension-2 sliding mode. Some results are expected, others come as a surprise. We are able to explain situations, where difficulties in numerical computations are reported in the recent literature. The analysis is based on asymptotic expansions for singularly perturbed problems and on the study of a time-parameterized two-dimensional dynamical system (hidden dynamics). Various situations are illustrated by examples.
Solutions leaving a codimension-2 sliding
GUGLIELMI, NICOLA;
2017-01-01
Abstract
Piece-wise smooth differential equations (their regularization, numerical integration, and classification of solutions) is the topic of the present work. The behaviour close to one discontinuity surface and also the entering into the intersection of two discontinuity surfaces is well understood. Here, we study the solutions that exit a codimension-2 sliding mode. Some results are expected, others come as a surprise. We are able to explain situations, where difficulties in numerical computations are reported in the recent literature. The analysis is based on asymptotic expansions for singularly perturbed problems and on the study of a time-parameterized two-dimensional dynamical system (hidden dynamics). Various situations are illustrated by examples.File | Dimensione | Formato | |
---|---|---|---|
2017_NonlinearDyn_88_Guglielmi.pdf
non disponibili
Tipologia:
Altro materiale allegato
Licenza:
Non pubblico
Dimensione
820.35 kB
Formato
Adobe PDF
|
820.35 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.