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求解Riesz空间分数阶扩散方程的一种新的数值方法

本站小编 Free考研考试/2021-12-27

杨晋平1, 李志强1, 闫玉斌2
1. 吕梁学院 数学系, 吕梁 033001;
2. 切斯特大学 数学系, 英国 CH1 4BJ
收稿日期:2017-07-28出版日期:2019-06-15发布日期:2019-05-18


基金资助:山西省自然科学基金(201801D121010)和吕梁学院校内基金(ZRXN201511)资助项目.


A NEW NUMERICAL METHOD FOR SOLVING RIESZ SPACE-FRACTIONAL DIFFUSION EQUATION

Yang Jinping1, Li Zhiqiang1, Yan Yubin2
1. Department of Mathematics, Luliang University, Lvliang 033001, China;
2. Department of Mathematics, University of Chester, Chester CH1 4BJ, UK
Received:2017-07-28Online:2019-06-15Published:2019-05-18







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本文利用Diethelm方法构造了一种逼近Riesz空间分数阶导数的O(△x3-α)格式,其中1 < α < 2,△x是空间步长.进一步对一阶时间导数采用Crank-Nicolson方法离散,得到了求解Riesz空间分数阶扩散方程的一种新的有限差分格式,并用矩阵方法证明了稳定性和收敛性,其误差估计为O(△t2+△x3-α),其中△t为时间步长.最后,数值算例验证了差分格式的正确性和有效性.
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