Eine Darstellung von Gleitbewegungen längs Unstetigkeitsflächen von Differentialgleichungen mit Sprungfunktionen

Mannshardt, Reinhold

doi:10.1002/zamm.19730531003

Cited by 3 publications

(2 citation statements)

References 5 publications

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“…[12] defines a more general solution which may slide along the switching space or along the intersection of several switching spaces. Sufficient conditions for such 'sliding solutions' are discussed by [18]. Practical examples to differential equations with bounded discontinuities can be found, e.g., in [17].…”

Section: Introductionmentioning

confidence: 99%

One-step methods of any order for ordinary differential equations with discontinuous right-hand sides

Mannshardt

1978

Numer. Math.

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Summary. The right-hand sides of a system of ordinary differential equations may be discontinuous on a certain surface. If a trajectory crossing this surface shall be computed by a one-step method, then a particular numerical analysis is necessary in a neighbourhood of the point of intersection. Such an analysis is presented in this paper. It shows that one can obtain any desired order of convergence if the method has an adequate order of consistency. Moreover, an asymptotic error theory is developed to justify Richardson extrapolation. A general one-step method is constructed satisfying the conditions of the preceding theory. Finally, a simplified Newton iteration scheme is used to implement this method.

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Section: Introductionmentioning

confidence: 99%

One-step methods of any order for ordinary differential equations with discontinuous right-hand sides

Mannshardt

1978

Numer. Math.

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“…Thus there is a point beyond which no classical solution exists (e.g [Fil64 ,Man73,. The question if the solution can cross the discontinuity can be answered by the sign of Dq+ and Dq-.…”

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confidence: 99%

Numerical Methods in Multibody Dynamics

Eich-Soellner¹,

Führer²

1998

European Consortium for Mathematics in Industry

274

121

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Within Europe a number of academic groups have accepted their responsibility towards European industry and have proposed to found a European Consortium for Mathematics in Industry (ECMI) as an expression of this responsibility. One of the activities of ECMI is the publication of books, which reflect its general philosophy; the texts of the series will help in promoting the use of mathematics in industry and in educating mathematicians for industry. They will consider different fields of applications, present casestudies, i'ntroduce new mathematical concepts in their (elation to practical applications. They shall also represent the variety of the European mathematical traditions, for example practical asymptotics and differential equations in Britian, sophisticated numerical analysis from France, powerful computation in Germany, novel discrete mathematics in Holland, elegant real analysis from Italy. They will demonstrate that all these branches of mathematics are applicable to real problems, and industry and universities in any country can clearly benefit from the skills of the complete range of European applied mathematics. All rights reservedNo part of this book may be reproduced by any means, or transmitted, or translated into a machine language without the written permission of the publisher.Cover design by Peter Pfitz Stuttgart.

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Numerische Behandlung von Zweipunktrandwertaufgaben für gewöhnliche Differentialgleichungssysteme erster Ordnung mit unstetiger rechter Seite

Glodde

1983

Z Angew Math Mech

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Die rechte Seite der Differentialgleichung sei unstetig auf gewissen Schaltflächen. Die Lösungen verstehen wir im Filippovschen Sinn. Es werden Bedingungen angegeben, unter denen der Verschiebeoperator des Systems stetig ist und lokal einer endlichen Familie von differenzierbaren Operatoren unterliegt. Mit dem Verschiebeoperator wird die Zweipunktrandwertaufgabe in eine Operatorgleichung im Rn übergeführt, in der der Operator dieselben Differenzierbarkeitseigenschaften hat wie der Verschiebeoperator. Für diese Klasse von Operatorgleichungen wird die Anwendbarkeit des Newton‐ und des Einbettungsverfahrens nachgewiesen. Der beim Einbettungsverfahren auftretende Homotopiepfad ist Lösung der Davidenko‐ Differentialgleichung im Sinne von Filippov. — Es wird die Anwendbarkeit der Verfahren auf das Problem der trockenen und zähen Reibung und das Tracking‐Problem der Optimalsteuerung diskutiert.

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Eine Darstellung von Gleitbewegungen längs Unstetigkeitsflächen von Differentialgleichungen mit Sprungfunktionen

Cited by 3 publications

References 5 publications

One-step methods of any order for ordinary differential equations with discontinuous right-hand sides

One-step methods of any order for ordinary differential equations with discontinuous right-hand sides

Numerical Methods in Multibody Dynamics

Numerische Behandlung von Zweipunktrandwertaufgaben für gewöhnliche Differentialgleichungssysteme erster Ordnung mit unstetiger rechter Seite

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