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Article information
2020 , Volume 25, ¹ 4, p.45-57
Paasonen V.I., Fedoruk M.P.
Improving the accuracy for numerical solutions of the Ginzburg - Landau equation
Increasing the order of accuracy for difference methods is an actual problem in nonlinear fiber optics. Computations, which use higher than the fourth order of accuracy by the direct construction of complex circuits on extended templates pose the complication of the system matrix and difficulties in setting additional boundary conditions. In addition, with this approach, there is no simultaneous increase in accuracy for the evolutionary variable. In this paper, we consider an alternative way, namely, application of the Richardson extrapolation, which reduces to construction of suitable linear combinations for solutions on various grids. This method allows improving the order of accuracy for both variables, while avoiding problems associated with the complication of templates, implementation of algorithms and setting additional boundary conditions. Double corrections are also considered to further improve accuracy. The technique was tested on exact solutions of the Ginzburg - Landau equation
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Keywords: order of accuracy, Schrodinger equation, Ginzburg - Landau equation, Richardson extrapolation, Runge correction
doi: 10.25743/ICT.2020.25.4.005
Author(s):
Paasonen Viktor Ivanovich
PhD. , Associate Professor
Position: Senior Research Scientist
Office: Federal Research Center for Information and Computational Technologies
Address: 630090, Russia, Novosibirsk, Ac. Lavrentiev ave. 6
Phone Office: (383) 330 86 56
E-mail: paas@ict.nsc.ru
Fedoruk Mikhail Petrovich
Dr. , Academician RAS, Professor
Position: Chancellor
Office: Novosibirsk State University, Federal Research Center for Information and Computational Technologies
Address: 630090, Russia, Novosibirsk, str. Pirogova, 2
Phone Office: (3832) 349105
E-mail: mife@net.ict.nsc.ru
SPIN-code: 4929-8753 References:
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Bibliography link:
Paasonen V.I., Fedoruk M.P. Improving the accuracy for numerical solutions of the Ginzburg - Landau equation // Computational technologies. 2020. V. 25. ¹ 4. P. 45-57
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