Generalisation of splitting methods based on modified potentials to nonlinear evolution equations of parabolic and Schrödinger type
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Show full item recordcomunitat-uji-handle:10234/9
comunitat-uji-handle2:10234/173364
comunitat-uji-handle3:10234/173369
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Title
Generalisation of splitting methods based on modified potentials to nonlinear evolution equations of parabolic and Schrödinger typeDate
2023-11-10Publisher
ElsevierBibliographic citation
BLANES, Sergio, et al. Generalisation of splitting methods based on modified potentials to nonlinear evolution equations of parabolic and Schrödinger type. Computer Physics Communications, 2024, vol. 295, p. 109007.Type
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Abstract
The present work is concerned with the extension of modified potential operator splitting methods to specific classes of nonlinear evolution equations. The considered partial differential equations of Schrödinger and ... [+]
The present work is concerned with the extension of modified potential operator splitting methods to specific classes of nonlinear evolution equations. The considered partial differential equations of Schrödinger and parabolic type comprise the Laplacian, a potential acting as multiplication operator, and a cubic nonlinearity. Moreover, an invariance principle is deduced that has a significant impact on the efficient realisation of the resulting modified operator splitting methods for the Schrödinger case.
Numerical illustrations for the time-dependent Gross–Pitaevskii equation in the physically most relevant case of three space dimensions and for its parabolic counterpart related to ground state and excited state computations confirm the benefits of the proposed fourth-order modified operator splitting method in comparison with standard splitting methods.
The presented results are novel and of particular interest from both, a theoretical perspective to inspire future investigations of modified operator splitting methods for other classes of nonlinear evolution equations and a practical perspective to advance the reliable and efficient simulation of Gross–Pitaevskii systems in real and imaginary time. [-]
Funder Name
Ministerio de Ciencia, Innovación y Universidades (Spain) | MCIN/AEI/10.13039/501100011033 | Generalitat Valenciana. Conselleria d'Innovació, Universitats, Ciència i Societat Digital
Project code
PID2019-104927GB-C21 | PID2019-104927GB-C22 | CIAICO/2021/180
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ERDF A way of making Europe
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© Copyright 2023 Elsevier B.V., All rights reserved.
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