TY - JOUR
T1 - Error control for time-splitting spectral approximations of the semiclassical Schrödinger 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 ∞(L2)-norm for time-splitting spectral methods applied to the linear Schrödinger 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 ∞(L2)-norm for time-splitting spectral methods applied to the linear Schrödinger 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 - Schrödinger equation
KW - time-splitting spectral methods
UR - http://www.scopus.com/inward/record.url?scp=79953675709&partnerID=8YFLogxK
U2 - 10.1093/imanum/drp044
DO - 10.1093/imanum/drp044
M3 - Article
AN - SCOPUS:79953675709
SN - 0272-4979
VL - 31
SP - 416
EP - 441
JO - IMA Journal of Numerical Analysis
JF - IMA Journal of Numerical Analysis
IS - 2
ER -