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Article information
2017 , Volume 22, ¹ 6, p.89-97
Smirnov S.V.
High-order step-split Fourier schemes for nonlinear Schrodinger equation
Purpose. The paper compares efficiency of high (up to 6th) order step-split Fourier schemes for nonlinear Schrodinger equation (NLSE) extensively used in telecom and laser physics. Methodology. Different step-split Fourier schemes of the second, fourth and sixth orders for nonlinear Schr¨odinger equation (NLSE) were implemented using custom C/C++ program code. Each scheme was used to integrate NLSE with solitons of different orders as initial conditions. It was carefully checked that all numerical solutions approximated the exact analytical ones. We used Runge method in order to find integration error what allowed us to eliminate contribution of temporal mesh step size. To estimate the integration error, the Runge method was used, which allowed eliminating the contribution of the t -grid pitch to the finiteness error. As a quantitative measure of the efficiency of splitting schemes, the numerical integration error calculated by the Runge method as a function of the number of discrete Fourier transforms is used in the paper. Findings. Optimum numerical splitting schemes were found depending on the required accuracy of the numerical solution and the order of the soliton (nonlinearity of the problem). In particular, it was established that for soliton of the second order a widely distributed symmetric numerical scheme of the second order is optimal for an accuracy not exceeding 10-4. For calculations with higher accuracy, the Blow-Wood scheme of the fourth order is preferred. In calculations with the accuracy higher than 10-7, we demonstrated that the sixth-order splitting scheme is advisable. Originality/value. Efficiency of step-split schemes of the sixth order was examined and for the first time compared with the schemes of the second and fourth order.
[full text]
Keywords: nonlinear Schrodinger equation, step-split Fourier method
Author(s):
Smirnov Sergey Valerievich
PhD.
Position: Senior Research Scientist
Office: Novosibirsk State University
Address: 630090, Russia, Novosibirsk, 2, Pirogova str.,
Phone Office: (383)3634165
E-mail: smirnov@lab.nsu.ru
SPIN-code: 6287-2781 References:
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Bibliography link:
Smirnov S.V. High-order step-split Fourier schemes for nonlinear Schrodinger equation // Computational technologies. 2017. V. 22. ¹ 6. P. 89-97
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