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In this paper we introduce numerical schemes for a one-dimensional kinetic model of the Boltzmann equation with dissipative collisions and variable coefficient of restitution. In particular, we study the numerical passage of the Boltzmann equation with singular kernel to nonlinear friction equations in the so-called quasi elastic limit. To this aim we introduce a Fourier spectral method for the Boltzmann equation [25, 26] and show that the kernel modes that define the spectral method have the correct...
In this paper we introduce numerical schemes for a
one-dimensional kinetic model of the Boltzmann equation with
dissipative collisions and variable coefficient of restitution. In
particular, we study the numerical passage of the Boltzmann
equation with singular kernel to nonlinear friction equations in
the so-called quasi elastic limit. To this aim we introduce a
Fourier spectral method for the Boltzmann equation [CITE]
and show that the kernel modes that define the spectral method
have the correct...
The aim of this work is to introduce and to analyze new algorithms for solving the
transport neutronique equation in 2D geometry. These algorithms present the duplicate favors to be,
on the one hand faster than some classic algorithms and easily to be implemented and naturally
deviced for parallelisation on the other hand. They are based on a splitting of the collision operator
holding amount of caracteristics of the transport operator. Some numerical results are given at the end
of this work.
...
Stability analysis for numerical solutions of Voltera integro-differential equations based on linear multistep methods combined with reducible quadrature rules is presented. The results given are based on the test equation and absolute stability is deffined in terms of the real parameters and . Sufficient conditions are illustrated for - methods and for combinations of Adams-Moulton and backward differentiation methods.
Among the applications of orthogonal polynomials described briefly on my previous visit to this Center [9, §3.2] were slowly convergent series whose terms could be represented in terms of the Laplace transform at integer arguments. We proposed to sum such series by means of Gaussian quadrature rules applied to suitable integrals involving weight functions of Einstein and Fermi type (cf. [13]). In the meantime it transpired that the technique is applicable to a large class of numerical series and,...
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