Time discretization of nonlinear hyperbolic systems on networks | Zendy

Altmann Robert | Zendy; Zimmer Christoph | Zendy

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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.

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