## Journals

- Advances in Mathematics of Communications
- Big Data & Information Analytics
- Communications on Pure & Applied Analysis
- Discrete & Continuous Dynamical Systems - A
- Discrete & Continuous Dynamical Systems - B
- Discrete & Continuous Dynamical Systems - S
- Evolution Equations & Control Theory
- Inverse Problems & Imaging
- Journal of Computational Dynamics
- Journal of Dynamics & Games
- Journal of Geometric Mechanics
- Journal of Industrial & Management Optimization
- Journal of Modern Dynamics
- Kinetic & Related Models
- Mathematical Biosciences & Engineering
- Mathematical Control & Related Fields
- Mathematical Foundations of Computing
- Networks & Heterogeneous Media
- Numerical Algebra, Control & Optimization
- AIMS Mathematics
- Conference Publications
- Electronic Research Announcements
- Mathematics in Engineering

### Open Access Journals

NHM

This paper is focused on continuum-discrete models for supply chains. In particular, we consider the model introduced in [10], where a system of conservation laws describe the evolution of the supply chain status on sub-chains, while at some nodes solutions are determined by Riemann solvers. Fixing the rule of flux maximization, two new Riemann Solvers are defined. We study the equilibria of the resulting dynamics, moreover some numerical experiments on sample supply chains are reported. We provide also a comparison, both of equilibria and experiments, with the model of [15].

keywords:
networks
,
conservation laws
,
fluid-dynamic models
,
finite difference schemes
,
Supply chains

NHM

We consider a mathematical model for fluid-dynamic flows on networks which is based on conservation laws. Road networks are considered as
graphs composed by arcs that meet at some junctions. The crucial point is
represented by junctions, where interactions occur and the problem is underdetermined. The approximation of scalar conservation laws along arcs is carried
out by using conservative methods, such as the classical Godunov scheme and
the more recent discrete velocities kinetic schemes with the use of suitable
boundary conditions at junctions. Riemann problems are solved by means of
a simulation algorithm which proceeds processing each junction. We present
the algorithm and its application to some simple test cases and to portions of
urban network.

DCDS-B

New computation algorithms for a fluid-dynamic mathematical model
of flows on networks are proposed, described and
tested.
First we improve the classical Godunov
scheme (G) for a special flux function,
thus obtaining a more efficient method, the Fast Godunov
scheme (FG) which reduces the number of evaluations for the numerical
flux.
Then a new method, namely the Fast Shock Fitting
method (FSF), based on good theorical properties of the solution of the
problem is introduced.
Numerical results and efficiency tests are presented in order to show the
behaviour of FSF in comparison with G, FG and a conservative
scheme of second order.

DCDS-S

In this paper we propose a Godunov-based discretization of a hyperbolic system of conservation laws with discontinuous flux, modeling vehicular flow on a network. Each equation describes the density evolution of vehicles having a common path along the network.
We show that the algorithm selects automatically an admissible solution at junctions, hence

*ad hoc*external procedures (e.g., maximization of the flux via a linear programming method) usually employed in classical approaches are no needed. Since users have not to deal explicitly with vehicle dynamics at junction, the numerical code can be implemented in minutes. We perform a detailed numerical comparison with a Godunov-based scheme coming from the classical theory of traffic flow on networks which maximizes the flux at junctions.
keywords:
LWR model
,
traffic flow
,
multipopulation model
,
Godunov scheme
,
multipath model
,
networks.

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