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Efficient Computation of the Nonlinear Schrödinger Equation with Time-Dependent Coefficients
Mathematics, Volume: 8, Issue: 3, Start page: 374
Swansea University Author:
Fabio Caraffini
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Copyright: 2020 by the authors. This is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license
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DOI (Published version): 10.3390/math8030374
Abstract
Motivated by the limited work performed on the development of computational techniques for solving the nonlinear Schrödinger equation with time-dependent coefficients, we develop a modified Runge–Kutta pair with improved periodicity and stability characteristics. Additionally, we develop a modified...
Published in: | Mathematics |
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ISSN: | 2227-7390 |
Published: |
MDPI AG
2020
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Online Access: |
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URI: | https://cronfa.swan.ac.uk/Record/cronfa60956 |
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Abstract: |
Motivated by the limited work performed on the development of computational techniques for solving the nonlinear Schrödinger equation with time-dependent coefficients, we develop a modified Runge–Kutta pair with improved periodicity and stability characteristics. Additionally, we develop a modified step size control algorithm, which increases the efficiency of our pair and all other pairs included in the numerical experiments. The numerical results on the nonlinear Schrödinger equation with a periodic solution verified the superiority of the new algorithm in terms of efficiency. The new method also presents a good behaviour of the maximum absolute error and the global norm in time, even after a high number of oscillations. |
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Keywords: |
nonlinear Schrödinger equation; periodic coefficients; varying dispersion; varying nonlinearity; Runge–Kutta pair; phase-lag; amplification error; step size control; local error estimation |
College: |
Faculty of Science and Engineering |
Funders: |
This research received no external funding. |
Issue: |
3 |
Start Page: |
374 |