Modified energy for split-step methods applied to the linear Schrödinger equation - Archive ouverte HAL
Article Dans Une Revue SIAM Journal on Numerical Analysis Année : 2009

Modified energy for split-step methods applied to the linear Schrödinger equation

Erwan Faou

Résumé

We consider the linear Schrödinger equation and its discretization by split-step methods where the part corresponding to the Laplace operator is approximated by the midpoint rule. We show that the numerical solution coincides with the exact solution of a modified partial differential equation at each time step. This shows the existence of a modified energy preserved by the numerical scheme. This energy is close to the exact energy if the numerical solution is smooth. As a consequence, we give uniform regularity estimates for the numerical solution over arbitrary long time
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Dates et versions

hal-00348221 , version 1 (18-12-2008)

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Arnaud Debussche, Erwan Faou. Modified energy for split-step methods applied to the linear Schrödinger equation. SIAM Journal on Numerical Analysis, 2009, 47 (5), pp.3705-3719. ⟨hal-00348221⟩
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