Efficient computation of the nonlinear schrodinger equation with time-dependent coefficients

Athinoula A. Kosti; Simon Colreavy-Donnelly; Fabio Caraffini; Zacharias A. Anastassi

doi:10.3390/math8030374

Efficient computation of the nonlinear schrodinger equation with time-dependent coefficients

Athinoula A. Kosti, Simon Colreavy-Donnelly, Fabio Caraffini, Zacharias A. Anastassi

De Montfort University

Research output: Contribution to journal › Article › peer-review

Abstract

Motivated by the limited work performed on the development of computational techniques for solving the nonlinear Schrodinger 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 Schrodinger 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.

Original language	English
Article number	374
Journal	Mathematics
Volume	8
Issue number	3
DOIs	https://doi.org/10.3390/math8030374
Publication status	Published - 1 Mar 2020
Externally published	Yes

Keywords

Amplification error
Local error estimation
Nonlinear schrödinger equation
Periodic coefficients
Phase-lag
Runge-kutta pair
Step size control
Varying dispersion
Varying nonlinearity

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10.3390/math8030374

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title = "Efficient computation of the nonlinear schrodinger equation with time-dependent coefficients",

abstract = "Motivated by the limited work performed on the development of computational techniques for solving the nonlinear Schrodinger 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 Schrodinger 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.",

keywords = "Amplification error, Local error estimation, Nonlinear schr{\"o}dinger equation, Periodic coefficients, Phase-lag, Runge-kutta pair, Step size control, Varying dispersion, Varying nonlinearity",

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T1 - Efficient computation of the nonlinear schrodinger equation with time-dependent coefficients

AU - Kosti, Athinoula A.

AU - Colreavy-Donnelly, Simon

AU - Caraffini, Fabio

AU - Anastassi, Zacharias A.

PY - 2020/3/1

Y1 - 2020/3/1

N2 - Motivated by the limited work performed on the development of computational techniques for solving the nonlinear Schrodinger 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 Schrodinger 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.

AB - Motivated by the limited work performed on the development of computational techniques for solving the nonlinear Schrodinger 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 Schrodinger 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.

KW - Amplification error

KW - Local error estimation

KW - Nonlinear schrödinger equation

KW - Periodic coefficients

KW - Phase-lag

KW - Runge-kutta pair

KW - Step size control

KW - Varying dispersion

KW - Varying nonlinearity

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U2 - 10.3390/math8030374

DO - 10.3390/math8030374

M3 - Article

AN - SCOPUS:85082415394

SN - 2227-7390

VL - 8

JO - Mathematics

JF - Mathematics

IS - 3

M1 - 374

ER -

Efficient computation of the nonlinear schrodinger equation with time-dependent coefficients

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Keywords

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