On a class of non-linear delay distributed order fractional diffusion equations

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• 作者：V.G. Pimenov^a ; ^b ; ^{vladimir.pimenov@urfu.ru} ; A.S. Hendy^b ; ^{ahmed.hendy@fsc.bu.edu.eg} ; R.H. De Staelen^c ; ^{rob.destaelen@ugent.be}
• 关键词：Distributed order fractional partial differential equations ; Difference scheme ; Discrete energy method ; Delay partial differential equations ; Convergence ; Stability
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：July 2017
• 年：2017
• 卷：318
• 期：Complete
• 页码：433-443
• 全文大小：451 K
• 卷排序：318

文摘

In this paper, we consider a numerical scheme for a class of non-linear time delay fractional diffusion equations with distributed order in time. This study covers the unique solvability, convergence and stability of the resulted numerical solution by means of the discrete energy method. The derivation of a linearized difference scheme with convergence order O(τ+(Δα)4+h4)O(τ+(Δα)4+h4) in L∞L∞-norm is the main purpose of this study. Numerical experiments are carried out to support the obtained theoretical results.