Abstract
The numerical solution of initial value problems with state-discontinuous right-hand sides by the well known implicit midpoint rule is discussed. The differential equations are transformed into differential inclusions following an approach of Filippov. The results are a theoretical foundation of the numerical treatment of problems arising in vehicle dynamics, mechanical systems with dry and Coulomb friction or population biology. An algorithm together with numerical tests is presented.
Zusammenfassung
In dieser Arbeit wird die Konvergenzordnung der impliziten Mittelpunktsregel angewandt auf Anfangswertprobleme mit unstetigen rechten Seiten untersucht. Die Differentialgleichungen werden nach der Theorie von Filippov in Differentialinklusionen transformiert. Die erzielten Resultate stellen eine theoretische Fundierung für die numerische Behandlung von Problemen aus der Fahrzeugdynamik, der Mechanik von Systemen mit trockener und Coulombscher Reibung oder aus der Populationsökologie dar. Ein Algorithmus und numerische Tests werden präsentiert.
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Kastner-Maresch, A.E. The implicit midpoint rule applied to discontinuous differential equations. Computing 49, 45–62 (1992). https://doi.org/10.1007/BF02238649
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DOI: https://doi.org/10.1007/BF02238649