Third order difference schemes (without using points outside of the domain) for one sided space tempered fractional partial differential equations
Third order difference schemes (without using points outside of the domain) for one sided space tempered fractional partial differential equations
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DOI：
10.1016/j.apnum.2016.10.011
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发表时间：
2017-02
影响因子：
2.8
通讯作者：
Yanyan Yu;W. Deng;Yujiang Wu;Jing Wu
中科院分区：
文献类型：
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作者：
Yanyan Yu;W. Deng;Yujiang Wu;Jing Wu
幂律概率密度函数（PDF）在次扩散和Lévy飞行中都起着关键作用。然而，有时由于粒子寿命的有限性或物理空间的有界性，回火幂律PDF似乎是一个更物理的选择，然后回火分数算子出现;事实上，回火分数算子也可以表征子扩散，正常扩散和Lévy飞行之间的转换。本文研究空间回火分数阶扩散方程的有限差分格式，这与纯分数阶导数的有限差分格式有很大的不同。利用矩阵的生成函数和Weyl定理，严格证明了所导出格式的稳定性和收敛性。数值模拟结果验证了所得到格式的有效性和数值精度。
Power-law probability density function (PDF) plays a key role in both subdiffusion and Lévy flights. However, sometimes because of the finiteness of the lifespan of the particles or the boundedness of the physical space, tempered power-law PDF seems to be a more physical choice and then the tempered fractional operators appear; in fact, the tempered fractional operators can also characterize the transitions among subdiffusion, normal diffusion, and Lévy flights. This paper focuses on the finite difference schemes for space tempered fractional diffusion equations, being much different from the ones for pure fractional derivatives. By using the generation function of the matrix and Weyl's theorem, the stability and convergence of the derived schemes are strictly proved. Some numerical simulations are performed to testify the effectiveness and numerical accuracy of the obtained schemes.