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Seasonal Forcing Drives Spatio-Temporal Pattern Formation in Rabies Epidemics

N. V. Festenberg, T. Gross, B. Blasius (2010)

Mathematical Modelling of Natural Phenomena

Seasonal forcing is identified as a key pattern generating mechanism in an epidemic model of rabies dispersal. We reduce an established individual-based high-detail model down to a deterministic conceptual model. The characteristic wave pattern characterized by high densities of infected individuals is maintained throughout the reduction process. In our model it is evident that seasonal forcing is the dominant factor that drives pattern formation. In particular we show that seasonal forcing can...

Set arithmetic and the enclosing problem in dynamics

Marian Mrozek, Piotr Zgliczyński (2000)

Annales Polonici Mathematici

We study the enclosing problem for discrete and continuous dynamical systems in the context of computer assisted proofs. We review and compare the existing methods and emphasize the importance of developing a suitable set arithmetic for efficient algorithms solving the enclosing problem.

Symmetric parareal algorithms for hamiltonian systems

Xiaoying Dai, Claude Le Bris, Frédéric Legoll, Yvon Maday (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The parareal in time algorithm allows for efficient parallel numerical simulations of time-dependent problems. It is based on a decomposition of the time interval into subintervals, and on a predictor-corrector strategy, where the propagations over each subinterval for the corrector stage are concurrently performed on the different processors that are available. In this article, we are concerned with the long time integration of Hamiltonian systems. Geometric, structure-preserving integrators are...

Symplectic local time-stepping in non-dissipative DGTD methods applied to wave propagation problems

Serge Piperno (2006)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The Discontinuous Galerkin Time Domain (DGTD) methods are now popular for the solution of wave propagation problems. Able to deal with unstructured, possibly locally-refined meshes, they handle easily complex geometries and remain fully explicit with easy parallelization and extension to high orders of accuracy. Non-dissipative versions exist, where some discrete electromagnetic energy is exactly conserved. However, the stability limit of the methods, related to the smallest elements in the mesh,...

Symplectic local time-stepping in non-dissipative DGTD methods applied to wave propagation problems

Serge Piperno (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

The Discontinuous Galerkin Time Domain (DGTD) methods are now popular for the solution of wave propagation problems. Able to deal with unstructured, possibly locally-refined meshes, they handle easily complex geometries and remain fully explicit with easy parallelization and extension to high orders of accuracy. Non-dissipative versions exist, where some discrete electromagnetic energy is exactly conserved. However, the stability limit of the methods, related to the smallest elements in the mesh,...

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