Отчет Нартикоев. Отчет по практике Вид практики Производственная (преддипломная) практика Выполнил студент
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ЗаключениеВ статье исследуется устойчивость и сходимость неявных разностных схем, аппроксимирующих пространственно-временное дробное уравнение конвекции-диффузии общего вида. Получены достаточные условия безусловной устойчивости таких разностных схем. Для доказательства устойчивости широкого класса разностных схем, аппроксимирующих уравнение дробной диффузии по времени, достаточно просто проверить условия устойчивости, полученные в данной статье. Между тем, новые разностные схемы второго построены также порядок аппроксимации по пространству и второй порядок аппроксимации по времени для ПВДУКД с переменными коэффициентами (в терминах t). Доказана устойчивость и сходимость этих неявных схем в сеточной L2-норме со скоростью, равной порядку ошибки аппроксимации. Метод может быть легко адаптирован к другим ПВДУКД с другими граничными условиями. Проведены численные испытания, полностью подтверждающие полученные теоретические результаты. Что еще более важно, с помощью (3.1) мы можем улучшить навыки вычислений за счет реализации надежных итерационных методов предварительного кондиционирования, с только вычислительными затратами и памятью в размере O (  ) и O ( ), соответственно. Обширные численные результаты сообщаются, чтобы проиллюстрировать эффективность предлагаемых методов предварительного кондиционирования. В будущей работе мы сосредоточимся на расширении предлагаемой НРС для обработки двух / трех - мерных ПВДУКД с помощью методов быстрого решения с учетом различных граничных значений. Между тем, мы также сосредоточимся на разработке других эффективных предобуславливателями для ускорения сходимости решателя подпространств Крылова для дискретизированных. Список литературы[1] I. Podlubny, Fractional Differential Equations, vol. 198 of Mathematics in Science and Engineering, Academic Press, Inc., San Diego, CA, 1999. [2] S.G. Samko, A.A. Kilbas, O.I. 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