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Hermite spline interpolation on patches for parallelly solving the Vlasov-Poisson equation

Nicolas Crouseilles, Guillaume Latu, Eric Sonnendrücker (2007)

International Journal of Applied Mathematics and Computer Science

This work is devoted to the numerical simulation of the Vlasov equation using a phase space grid. In contrast to Particle-In-Cell (PIC) methods, which are known to be noisy, we propose a semi-Lagrangian-type method to discretize the Vlasov equation in the two-dimensional phase space. As this kind of method requires a huge computational effort, one has to carry out the simulations on parallel machines. For this purpose, we present a method using patches decomposing the phase domain, each patch being...

Heteroclinic orbits in plane dynamical systems

Luisa Malaguti, Cristina Marcelli (2002)

Archivum Mathematicum

We consider general second order boundary value problems on the whole line of the type u ' ' = h ( t , u , u ' ) , u ( - ) = 0 , u ( + ) = 1 , for which we provide existence, non-existence, multiplicity results. The solutions we find can be reviewed as heteroclinic orbits in the ( u , u ' ) plane dynamical system.

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