Efficient Splitting Methods Based on Modified Potentials: Numerical Integration of Linear Parabolic Problems and Imaginary Time Propagation of the Schrödinger Equation
Year: 2023
Author: Sergio Blanes, Fernando Casas, Cesáreo González, Mechthild Thalhammer
Communications in Computational Physics, Vol. 33 (2023), Iss. 4 : pp. 937–961
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2022-0247
Communications in Computational Physics, Vol. 33 (2023), Iss. 4 : pp. 937–961
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 25
Keywords: Schrödinger equation imaginary time propagation parabolic equations operator splitting methods modified potentials.