caa a22 4500 605497109 CHVBK 20210128100539.0 cr unu---uuuuu 210128e20151201xx s 000 0 eng 10.1007/s10543-014-0538-5 doi (NATIONALLICENCE)springer-10.1007/s10543-014-0538-5 One-sided direct event location techniques in the numerical solution of discontinuous differential systems [Elektronische Daten] [Luca Dieci, Luciano Lopez] In this paper, event location techniques for a differential system the solution of which is directed towards a manifold $$\varSigma $$ Σ defined as the 0-set of a smooth function $$h: \varSigma =\{x\in \mathbb {R}^n\,:\, h(x)=0 \}$$ h : Σ = { x ∈ R n : h ( x ) = 0 } are considered. It is assumed that the exact solution trajectory hits $$\varSigma $$ Σ non-tangentially, and numerical techniques guaranteeing that the trajectory approaches $$\varSigma $$ Σ from one side only (i.e., does not cross it) are studied. Methods based on Runge Kutta schemes which arrive to $$\varSigma $$ Σ in a finite number of steps are proposed. The main motivation of this paper comes from integration of discontinuous differential systems of Filippov type, where location of events is of paramount importance. Springer Science+Business Media Dordrecht, 2014 Event manifold nationallicence Time reparametrization nationallicence Runge Kutta methods nationallicence Monotone integration nationallicence Dieci Luca School of Mathematics, Georgia Institute of Technology, 30332-0160, Atlanta, GA, USA aut Lopez Luciano Dipartimento di Matematica, Universitá degli Studi di Bari "Aldo Moro”, Via E. Orabona 4, 70125, Bari, Italy aut BIT Numerical Mathematics Springer Netherlands 55/4(2015-12-01), 987-1003 0006-3835 55:4<987 2015 55 10543 https://doi.org/10.1007/s10543-014-0538-5 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10543-014-0538-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Dieci Luca School of Mathematics, Georgia Institute of Technology, 30332-0160, Atlanta, GA, USA aut NATIONALLICENCE 700 1- Lopez Luciano Dipartimento di Matematica, Universitá degli Studi di Bari "Aldo Moro”, Via E. Orabona 4, 70125, Bari, Italy aut NATIONALLICENCE 773 0- BIT Numerical Mathematics Springer Netherlands 55/4(2015-12-01), 987-1003 0006-3835 55:4<987 2015 55 10543