论文摘要
最近,[Hou and Deng,J.Phys.A:Math.Theor.,51,155001（2018）]推导了一种向后的带有反应扩散项的Feynman-Kac方程,本文对该方程的二维情形提出了一个有限差分离散格式.数值求解该方程的关键在于如何离散时间回火分数阶物质导数和回火的分数阶Laplacian两类非局部算子.这里,我们利用了卷积求积方法来离散时间回火分数阶物质导数,得到一阶和二阶的离散格式,该方法最大的优点是不需要假设解关于时间的正则性;然后利用有限差分方法逼近了二维的回火分数阶Laplacian算子,而且其离散精度仅依赖于解在区域ˉ?上的正则性而不是全空间的正则性.最后,我们通过数值实验验证了预计的收敛阶及算法的有效性.
论文目录
文章来源
类型: 硕士论文
作者: 聂大鑫
导师: 邓伟华
关键词: 二维的方程,有限差分逼近,卷积求积,误差估计
来源: 兰州大学
年度: 2019
分类: 基础科学
专业: 数学,数学
单位: 兰州大学
分类号: O241.8
总页数: 51
文件大小: 1627K
下载量: 30
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