| Инд. авторы: | Паасонен В.И., Федорук М.П. |
| Заглавие: | Трехслойная безытерационная схема повышенного порядка точности для уравнения Гинзбурга-Ландау |
| Библ. ссылка: | Паасонен В.И., Федорук М.П. Трехслойная безытерационная схема повышенного порядка точности для уравнения Гинзбурга-Ландау // Вычислительные технологии. - 2015. - Т.20. - № 3. - С.46-57. - ISSN 1560-7534. - EISSN 2313-691X. |
| Внешние системы: | РИНЦ: 23757839; |
| Реферат: | rus: Компактная разностная схема для уравнения Шрёдингера, ранее построенная и исследованная авторами, обобщается на случай уравнения Гинзбура - Ландау. Построенная схема трехслойная, с нелинейностью на среднем слое, и поэтому не требует итераций по нелинейности. В работе приводятся результаты расчетов тестовых задач на последовательности сгущающихся сеток в сравнении с результатами, полученными по модифицированной схеме Кранка - Николсон второго порядка аппроксимации. eng: This paper presents a generalization of compact difference scheme previously developed and investigated by the authors for one-dimensional nonlinear Schrödinger equation to the case of the Ginzburg -Landau equation. We apply the increased order of accuracy as a very useful tool for improvement of the quality of calculations. The scheme approximates the Ginzburg-Landau equation with the second-order for the evolutionary variable and with the fourth order for the "slow time". The scheme is essentially of a two-level, but the scheme uses a double step at three levels, with the non-linear approximation on the right side at the middle level. This approach do not require the need to iterate on the nonlinearity at all steps, except the first, and thus saves computing resources. To compute the solution in the first step we proposed to use a two-level iterative scheme providing the same order of approximation as for the main scheme. Stability of difference schemes was examined in the linear approximation using the analysis of variance of the behavior harmonics. The paper presents the results of calculations on the sequence of the test problems which use the condensing grids with known exact solutions obtained earlier by Ahmediev and Afanasiev in their famous work. A comparison with the results obtained by the three-layered modified Crank-Nicolson scheme with approximation of the second order. The above graphic and tabular material evidence of significant advantages of a compact difference scheme. |
| Ключевые слова: | нелинейная волоконная оптика; повышенный порядок точности; компактная разностная схема; уравнение Шредингера; уравнение Гинзбурга - Ландау; fiber laser; Nonlinear fiber optics; high-order accuracy scheme; Compact difference scheme; Shrödinger equation; Ginzburg Landau equation; волоконный лазер; |
| Издано: | 2015 |
| Физ. характеристика: | с.46-57 |
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