High accuracy finite difference schemes for fractional sub-diffusionequations

报告题目:High accuracy finite difference schemes for fractional sub-diffusionequations

报告人:纪翠翠,东南大学数学学院计算数学专业博士

时间:2017 年 6 月 20 号 10:00-11:00

地点:知新楼 B 座 1044 报告厅

摘要:

During the past several decades, the study of fractional partial differential equations (FPDEs) has attracted many scholars’ attention. The most important reason is that the FPDEs can be more accurate than the classical integer order differential equations in the description of some physical and chemical processes because the fractional operators enjoy the nonlocal connectivity. In this talk, based on the weighted and shifted Gr nwald operator, a high order compact finite difference scheme is derived for the 1D fractional sub-diffusion equation. It is proved that the difference scheme is unconditionally stable and convergent by the energy method. For all (0,0.956), the convergence order is , where is the temporal step size and is the spatial step size. Then the extension to the 2D case is taken into account. Finally, some numerical examples are given to confirm the theoretical results.