ОПТИМИЗАЦИОННЫЙ АЛГОРИТМ ДЛЯ ЧИСЛЕННОЙ РЕАЛИЗАЦИИ ДРОБНОЙ ПРОИЗВОДНОЙ ГРЮНВАЛЬДА-ЛЕТНИКОВА НА ОСНОВЕ ПРИНЦИПА МЕМОИЗАЦИИ ДЛЯ ОБЫКНОВЕННЫХ ДИФФЕРЕНЦИАЛЬНЫХ УРАВНЕНИЙ

Дробные производные благодаря своей нелокальности могут описывать сложные процессы, где исторические данные важны для будущих вычислений. Одновременно данное свойство приносит трудности при численных моделированиях. Эта статья представляет новый дискретный оператор для аппроксимации дробной производной на основе определения Грюнвальда-Летникова, «принципа короткой памяти», мемоизации и аналитических предположений. Данный оператор существенно уменьшает количество операций в процессе вычислений, при решении краевых задач, за счет сохранения вычисляемых данных и преобразования для дальнейшего использования с регулируемой точностью.

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