135 research outputs found
Bernoulli type polynomials on Umbral Algebra
The aim of this paper is to investigate generating functions for modification
of the Milne-Thomson's polynomials, which are related to the Bernoulli
polynomials and the Hermite polynomials. By applying the Umbral algebra to
these generating functions, we provide to deriving identities for these
polynomials
A characteristic particle method for traffic flow simulations on highway networks
A characteristic particle method for the simulation of first order
macroscopic traffic models on road networks is presented. The approach is based
on the method "particleclaw", which solves scalar one dimensional hyperbolic
conservations laws exactly, except for a small error right around shocks. The
method is generalized to nonlinear network flows, where particle approximations
on the edges are suitably coupled together at the network nodes. It is
demonstrated in numerical examples that the resulting particle method can
approximate traffic jams accurately, while only devoting a few degrees of
freedom to each edge of the network.Comment: 15 pages, 5 figures. Accepted to the proceedings of the Sixth
International Workshop Meshfree Methods for PDE 201
The Gould-Hopper Polynomials in the Novikov-Veselov equation
We use the Gould-Hopper (GH) polynomials to investigate the Novikov-Veselov
(NV) equation. The root dynamics of the -flow in the NV equation is
studied using the GH polynomials and then the Lax pair is found. In particulr,
when , one can get the Gold-fish model. The smooth rational solutions
of the NV equation are also constructed via the extended Moutard transformation
and the GH polynomials. The asymptotic behavior is discussed and then the
smooth rational solution of the Liouville equation is obtained.Comment: 22 pages, no figur
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