Solving the nonlinear Schrödinger equation using exponential integrators
Using the notion of integrating factors, Lawson developed a class of numerical methods for solving stiff systems of ordinary differential equations. However, the performance of these "Generalized Runge - Kutta processes" was demonstrably poorer when compared to the ETD schemes of Certaine...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Norwegian Society of Automatic Control
2006-10-01
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| Series: | Modeling, Identification and Control |
| Subjects: | |
| Online Access: | http://www.mic-journal.no/PDF/2006/MIC-2006-4-1.pdf |
| _version_ | 1818119206336462848 |
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| author | Håvard Berland Brynjulf Owren Bård Skaflestad |
| author_facet | Håvard Berland Brynjulf Owren Bård Skaflestad |
| author_sort | Håvard Berland |
| collection | DOAJ |
| description | Using the notion of integrating factors, Lawson developed a class of numerical methods for solving stiff systems of ordinary differential equations. However, the performance of these "Generalized Runge - Kutta processes" was demonstrably poorer when compared to the ETD schemes of Certaine and Nørsett, recently rediscovered by Cox and Matthews. The deficit is particularly pronounced when the schemes are applied to parabolic problems. In this paper we compare a fourth order Lawson scheme and a fourth order ETD scheme due to Cox and Matthews, using the nonlinear Schro¨dinger equation as the test problem. The primary testing parameters are degree of regularity of the potential function and the initial condition, and numerical performance is heavily dependent upon these values. The Lawson and ETD schemes exhibit significant performance differences in our tests, and we present some analysis on this. |
| first_indexed | 2024-12-11T05:06:31Z |
| format | Article |
| id | doaj.art-f93b59e886e946e48518b4919950fc9d |
| institution | Directory Open Access Journal |
| issn | 0332-7353 1890-1328 |
| language | English |
| last_indexed | 2024-12-11T05:06:31Z |
| publishDate | 2006-10-01 |
| publisher | Norwegian Society of Automatic Control |
| record_format | Article |
| series | Modeling, Identification and Control |
| spelling | doaj.art-f93b59e886e946e48518b4919950fc9d2022-12-22T01:20:01ZengNorwegian Society of Automatic ControlModeling, Identification and Control0332-73531890-13282006-10-0127420121810.4173/mic.2006.4.1Solving the nonlinear Schrödinger equation using exponential integratorsHåvard BerlandBrynjulf OwrenBård SkaflestadUsing the notion of integrating factors, Lawson developed a class of numerical methods for solving stiff systems of ordinary differential equations. However, the performance of these "Generalized Runge - Kutta processes" was demonstrably poorer when compared to the ETD schemes of Certaine and Nørsett, recently rediscovered by Cox and Matthews. The deficit is particularly pronounced when the schemes are applied to parabolic problems. In this paper we compare a fourth order Lawson scheme and a fourth order ETD scheme due to Cox and Matthews, using the nonlinear Schro¨dinger equation as the test problem. The primary testing parameters are degree of regularity of the potential function and the initial condition, and numerical performance is heavily dependent upon these values. The Lawson and ETD schemes exhibit significant performance differences in our tests, and we present some analysis on this.http://www.mic-journal.no/PDF/2006/MIC-2006-4-1.pdfExponential integratorsnonlinear Schro¨dinger equationregularity requirements |
| spellingShingle | Håvard Berland Brynjulf Owren Bård Skaflestad Solving the nonlinear Schrödinger equation using exponential integrators Modeling, Identification and Control Exponential integrators nonlinear Schro¨dinger equation regularity requirements |
| title | Solving the nonlinear Schrödinger equation using exponential integrators |
| title_full | Solving the nonlinear Schrödinger equation using exponential integrators |
| title_fullStr | Solving the nonlinear Schrödinger equation using exponential integrators |
| title_full_unstemmed | Solving the nonlinear Schrödinger equation using exponential integrators |
| title_short | Solving the nonlinear Schrödinger equation using exponential integrators |
| title_sort | solving the nonlinear schrodinger equation using exponential integrators |
| topic | Exponential integrators nonlinear Schro¨dinger equation regularity requirements |
| url | http://www.mic-journal.no/PDF/2006/MIC-2006-4-1.pdf |
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