TY - JOUR
T1 - Efficient Splitting Methods Based on Modified Potentials: Numerical Integration of Linear Parabolic Problems and Imaginary Time Propagation of the Schrödinger Equation
AU - Blanes , Sergio
AU - Casas , Fernando
AU - González , Cesáreo
AU - Thalhammer , Mechthild
JO - Communications in Computational Physics
VL - 4
SP - 937
EP - 961
PY - 2023
DA - 2023/05
SN - 33
DO - http://doi.org/10.4208/cicp.OA-2022-0247
UR - https://global-sci.org/intro/article_detail/cicp/21665.html
KW - Schrödinger equation, imaginary time propagation, parabolic equations, operator splitting methods, modified potentials.
AB - <p style="text-align: justify;">We present a new family of fourth-order splitting methods with positive coefficients especially tailored for the time integration of linear parabolic problems and,
in particular, for the time dependent Schrödinger equation, both in real and imaginary
time. They are based on the use of a double commutator and a modified processor, and
are more efficient than other widely used schemes found in the literature. Moreover,
for certain potentials, they achieve order six. Several examples in one, two and three
dimensions clearly illustrate the computational advantages of the new schemes.</p>