Error control for time-splitting spectral approximations of the semiclassical Schrodinger equation

TY - JOUR

T1 - Error control for time-splitting spectral approximations of the semiclassical Schrodinger equation

AU - Kyza, Irene

AU - Makridakis, Charalambos

AU - Plexousakis, Michael

PY - 2011/4

Y1 - 2011/4

N2 - We prove a posteriori error estimates of optimal order in the L(infinity)(L(2))-norm for time-splitting spectral methods applied to the linear Schrodinger equation in the semiclassical regime. The a posteriori error estimates are obtained by considering an appropriate extension in time of the numerical schemes and using energy techniques. Numerical experiments are presented that confirm our theoretical results.

AB - We prove a posteriori error estimates of optimal order in the L(infinity)(L(2))-norm for time-splitting spectral methods applied to the linear Schrodinger equation in the semiclassical regime. The a posteriori error estimates are obtained by considering an appropriate extension in time of the numerical schemes and using energy techniques. Numerical experiments are presented that confirm our theoretical results.

KW - a posteriori estimates

KW - time-splitting spectral methods

KW - Schrodinger equation

U2 - 10.1093/imanum/drp044

DO - 10.1093/imanum/drp044

M3 - Article

SN - 0272-4979

VL - 31

SP - 416

EP - 441

JO - IMA Journal of Numerical Analysis

JF - IMA Journal of Numerical Analysis

IS - 2

ER -