Discrete approximations and periodic solutions of differential inclusions

Discrete approximations and periodic solutions of differential inclusions

We consider two numerical methods for solving a periodic boundary value problem for a system of differential inclusions, the Galerkin method and the polygon method. To the original problem, we assign a sequence of its discretizations. Conditions under which the existence of solutions of the periodic...

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Veröffentlicht in:Differential equations 2013-02, Vol.49 (2), p.235-245
Hauptverfasser: Klimov, V. S., Dem’yankov, N. A.
Format: Artikel
Sprache:eng
Schlagworte:
Approximation
Banach spaces
Bibliographic literature
Boundary value problems
Convergence
Difference and Functional Equations
Differential equations
Galerkin methods
Inclusions
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Methods
Numerical analysis
Numerical Methods
Ordinary Differential Equations
Partial Differential Equations
Studies
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Beschreibung
Zusammenfassung:We consider two numerical methods for solving a periodic boundary value problem for a system of differential inclusions, the Galerkin method and the polygon method. To the original problem, we assign a sequence of its discretizations. Conditions under which the existence of solutions of the periodic boundary value problem implies the solvability of its discrete versions are presented. The convergence of the sequence of approximate solutions is analyzed.
ISSN:0012-2661
1608-3083
DOI:10.1134/S0012266113020109