Implicit runge-kutta methods for differential inclusions

1 January 1990

journal article
research article
Published by Taylor & Francis in Numerical Functional Analysis and Optimization

Vol. 11 (9-10) , 937-958
https://doi.org/10.1080/01630569108816411

Abstract

This paper is concerned with the application of implicit Runge-Kutta methods suitable for stiff initial value problems to initial value problems for differential inclusions with upper semicontinuous right-hand sides satisfying a uniform one-sided Lipschitz condition and a growth condition. The problems could stem from differential equations with state discontinuous right-hand sides. It is shown that there exist methods with higher order of convergence on intervals where the solution is smooth enough. Globally we get at least the order one.

Keywords

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