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
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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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description 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.
doi_str_mv 10.1137/080729049
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subjects Applied mathematics
Boltzmann Vlasov equation
Copyright
Error bounds
Errors
Interpolation
Mathematical models
Mathematics
Methods
Numerical analysis
Relativistic particles
Splines
Splitting
Vlasov equations
title HIGHER ORDER TIME SPLITTING FOR THE LINEAR VLASOV EQUATION
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