HIGHER ORDER TIME SPLITTING FOR THE LINEAR VLASOV EQUATION

HIGHER ORDER TIME SPLITTING FOR THE LINEAR VLASOV EQUATION

Many semi-Lagrangian schemes for solving the Vlasov equation use a second order time splitting method proposed by Cheng and Knorr. In this paper a fourth order time splitting method is proposed. This is combined with cubic spline interpolation (in x and v), and a rigorous ℓ 2 error bound is obtained...

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Veröffentlicht in:SIAM journal on numerical analysis 2009-01, Vol.47 (3), p.2203-2223
1. Verfasser: SCHAEFFER, JACK
Format: Artikel
Sprache:eng
Schlagworte:
Applied mathematics
Boltzmann Vlasov equation
Copyright
Error bounds
Errors
Interpolation
Mathematical models
Mathematics
Methods
Numerical analysis
Relativistic particles
Splines
Splitting
Vlasov equations
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Beschreibung
Zusammenfassung:Many semi-Lagrangian schemes for solving the Vlasov equation use a second order time splitting method proposed by Cheng and Knorr. In this paper a fourth order time splitting method is proposed. This is combined with cubic spline interpolation (in x and v), and a rigorous ℓ 2 error bound is obtained for the linear Vlasov equation in arbitrary space dimension. Also, this method and that of Cheng and Knorr are implemented and compared for a test case in one space dimension.
ISSN:0036-1429
1095-7170
DOI:10.1137/080729049