The MWF method: A convergence theorem for homogeneous one-dimensional case

Authors:
Carlo Bianca;Santo Motta
Affiliations:
Department of Mathematics and Computer Science, University of Catania, Italy;Department of Mathematics and Computer Science, University of Catania, Italy
Venue:
Computers & Mathematics with Applications
Year:
2009

Citing 10
Cited 0

Computer simulation using particles

Computer simulation using particles
A new numerical method for kinetic equations in several dimensions

Computing
Parallel efficiency of the C.R.F. method on an IBM RS/6000 cluster platform

Journal of Scientific Computing
A stochastic weighted particle method for the Boltzmann equation

Journal of Computational Physics
Reduction of the number of particles in the stochastic weighted particle method for the Boltzmann equation

Journal of Computational Physics
Optimal vaccination schedules using simulated annealing

Bioinformatics
The MWF method for kinetic equations system

Computers & Mathematics with Applications
Meshfree Particle Methods

Meshfree Particle Methods
Genetic algorithm against cancer

WILF'05 Proceedings of the 6th international conference on Fuzzy Logic and Applications
A new formulation and gauge invariance of the MW-CRF method for kinetic equations

Mathematical and Computer Modelling: An International Journal

Quantified Score

Hi-index	0.09

Visualization

Abstract

The MWF numerical method for kinetic equations was presented by S. Motta and J. Wick in 1992 and recently extended by the authors to systems of kinetic equations. The basic idea of the method consists in rewriting the kinetic equation in a conservation law in divergence form, redefining the collisions as a flux and formally to transform the problem into a collisionless one. In all tested cases, the numerical results are in agreement with the exact solutions but a convergence proof of the method, to the best of our knowledge, is missing. In this paper we present our investigation on the sufficient conditions that the collision operator may satisfy, to guarantee a convergence proof of the method in the homogeneous one-dimensional case. This investigation is of both theoretical and applied interest.