Time discretization of nonlinear hyperbolic systems on networks. Issue 1 (18th November 2019)

• Record Type: Journal Article
• Authors: Altmann, Robert; Zimmer, Christoph
• Other Names: Eberhardsteiner J. guestEditor.; Schöberl M. guestEditor.
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 19:Issue 1(2019)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2019-11-18
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201900057
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: In view of gas networks, the simulation of hyperbolic systems on networks has recently caused large interest. We consider the case with a nonlinear damping term and a small parameter ϵ such that – in the linear case – the system turns parabolic for ϵ =0. Based on this property and an expansion in ϵ, we derive a novel time integration scheme.