Third order difference schemes (without using points outside of the domain) for one sided space tempered fractional partial differential equations

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• 作者：Yanyan Yu^a ; ^b ; Weihua Deng^a ; ^{dengwh@lzu.edu.cn} ; Yujiang Wu^a ; Jing Wu^a
• 关键词：Tempered fractional calculus ; Finite difference schemes ; Riemann&ndash ; Liouville normalized tempered fractional derivative
• 刊名：Applied Numerical Mathematics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：112
• 期：Complete
• 页码：126-145
• 全文大小：446 K
• 卷排序：112

文摘

For biological particles, the tempered power-law diffusions, instead of pure power-law diffusion, are the more general observed experimental phenomena. The schemes of the tempered models and their proof of the stability and convergence are much different from the ones of the corresponding non-tempered ones. Third-order quasi-compact schemes are derived with strict convergence and stability proof for the tempered model. The generation function of the matrix and Weyl's theorem play important role in the proof of convergence and stability.