Чисельне розв’язання рівняння субдифузії змінного порядку в багатовимірному просторі
Subdiffusion equation in a bounded domain of a multidimensional Euclidian space is considered. The equation contains a fractional Riemann-Liouville time derivative, with order that depends on space, and is under the Laplace operator, that corresponds to the equation, obtain...
Збережено в:
| Дата: | 2023 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | Українська |
| Опубліковано: |
Інститут прикладних проблем механіки і математики ім. Я. С. Підстригача НАН України
2023
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| Теми: | |
| Онлайн доступ: | https://www.fmmit.lviv.ua/index.php/fmmit/article/view/320 |
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| Назва журналу: | Physico-mathematical modeling and informational technologies |
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Репозитарії
Physico-mathematical modeling and informational technologies| Резюме: | Subdiffusion equation in a bounded domain of a multidimensional Euclidian space is considered. The equation contains a fractional Riemann-Liouville time derivative, with order that depends on space, and is under the Laplace operator, that corresponds to the equation, obtained from the process of continuous-time random walk. A transformation of this equation to a subdiffusion equation with homogeneous initial condition, that contains a fractional Caputo derivative, is suggested. Since for each fixed time moment a subdiffusion equation turns into a well-studied elliptic partial differential equation, finite difference time approximation of transformed subdiffusion equation is built. Theorem about stability and convergence of the half-discretized (discretized in time, continuous in space) scheme in quadratic norm is given for a sufficiently smooth solution. |
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