Close Search Advanced
Journals
Resources
About Us
Open Access

Efficient Splitting Methods Based on Modified Potentials: Numerical Integration of Linear Parabolic Problems and Imaginary Time Propagation of the Schrödinger Equation

Efficient Splitting Methods Based on Modified Potentials: Numerical Integration of Linear Parabolic Problems and Imaginary Time Propagation of the Schrödinger Equation
Preview
Add to basket

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.

Submit Article

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

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.

Author Details

Sergio Blanes

Fernando Casas

Cesáreo González

Mechthild Thalhammer

  1. New efficient numerical methods for some systems of linear ordinary differential equations

    Boda, Lívia | Faragó, István

    Mathematics and Computers in Simulation, Vol. (2024), Iss.

    https://doi.org/10.1016/j.matcom.2024.10.030 [Citations: 0]

  2. Generalisation of splitting methods based on modified potentials to nonlinear evolution equations of parabolic and Schrödinger type

    Blanes, S. | Casas, F. | González, C. | Thalhammer, M.

    Computer Physics Communications, Vol. 295 (2024), Iss. P.109007

    https://doi.org/10.1016/j.cpc.2023.109007 [Citations: 0]

  3. Families of efficient low order processed composition methods

    Blanes, S. | Casas, F. | Escorihuela-Tomàs, A.

    Applied Numerical Mathematics, Vol. 204 (2024), Iss. P.86

    https://doi.org/10.1016/j.apnum.2024.06.002 [Citations: 1]