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Time discretization of nonlinear hyperbolic systems on networks
Author(s) -
Altmann Robert,
Zimmer Christoph
Publication year - 2019
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201900057
Subject(s) - nonlinear system , discretization , property (philosophy) , scheme (mathematics) , term (time) , mathematics , hyperbolic partial differential equation , mathematical analysis , computer science , control theory (sociology) , physics , partial differential equation , artificial intelligence , philosophy , control (management) , epistemology , quantum mechanics
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.