Numerical integration methods of the Vlasov equation

Numerical convergence in solving the Vlasov equation.

When the Vlasov equation is investigated numerically using the method of test particles, the two-body interactions that inevitably arise in the simulation (but are not present in the Vlasov equation itself) drive the collection of test particles toward a state of classical thermal equilibrium. We estimate the relaxation time associated with this thermalization. The Vlasov equation plays a centr...

Conservative Numerical Schemesfor the Vlasov Equation

Conservative Numerical Schemes for the Vlasov Equation Francis Filbet,∗ Eric Sonnendrücker,† and Pierre Bertrand‡ ∗IECN–INRIA Project Numath, Université de Nancy I, BP 239, 54506 Vandœuvre-lès-Nancy Cedex, France; †IRMA, Université Louis Pasteur, 7 Rue R Descartes, 67084 Strasbourg, France; and ‡LPMI, Université de Nancy I, BP 239, 54506 Vandœuvre-lès-Nancy Cedex, France E-mail: [email protected]...

Streamline diffusion methods for the Vlasov-Poisson equation

— We prove error estimâtes for the streamline diffusion and the discontinuous Galerkin finite element methods for discretization of the Vlasov-Poisson équation. Résumé. — Nous démontrons des estimations d'erreur pour la méthode de Galerkin discontinue pour la discrétisation de l'équation de Vlasov-Poisson.

Numerical Solution of Sawada-Kotera equation by using Iterative Methods

NUMERICAL SOLUTION OF INTEGRO-DIFFERENTIAL EQUATION BY USING CHEBYSHEV WAVELET OPERATIONAL MATRIX OF INTEGRATION

In this paper, we propose a method to approximate the solution of a linear Fredholm integro-differential equation by using the Chebyshev wavelet of the first kind as basis. For this purpose, we introduce the first Chebyshev operational matrix of integration. Chebyshev wavelet approximating method is then utilized to reduce the integro-differential equation to a system of algebraic equations. Il...