Osman, S. A and Langlands, T. A. M. (2019) An implicit Keller Box numerical scheme for the solution of fractional subdiffusion equations. Applied Mathematics and Computation, 348. pp. 609626. ISSN 00963003

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Abstract
In this work, we present a new implicit numerical scheme for fractional subdiffusion equations. In this approach we use the Keller Box method [1] to spatially discretise the fractional subdiffusion equation and we use a modified L1 scheme (ML1), similar to the L1 scheme originally developed by Oldham and Spanier [2], to approximate the fractional derivative. The stability of the proposed method was investigated by using VonNeumann stability analysis. We have proved the method is unconditionally stable when $0<{\lambda}_q <\min(\frac{1}{\mu_0},2^\gamma)$ and $0<\gamma \le 1$, and demonstrated the method is also stable numerically in the case $\frac{1}{\mu_0}<{\lambda}_q \le 2^\gamma$ and $\log_3{2} \le \gamma \le 1$. The accuracy and convergence of the scheme was also investigated and found to be of order $O(\Delta t^{1+\gamma})$ in time and $O(\Delta x^2)$ in space. To confirm the accuracy and stability of the proposed method we provide three examples with one including a linear reaction term.
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Item Type:  Article (Commonwealth Reporting Category C) 

Refereed:  Yes 
Item Status:  Live Archive 
Additional Information:  Published version cannot be displayed due to copyright restrictions. 
Faculty/School / Institute/Centre:  Current  Faculty of Health, Engineering and Sciences  School of Agricultural, Computational and Environmental Sciences 
Date Deposited:  21 May 2019 04:33 
Last Modified:  13 Jun 2019 02:02 
Uncontrolled Keywords:  fractional subdiffusion equation, Keller Box method, fractional calculus, L1 scheme, linear reaction 
Fields of Research :  01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010302 Numerical Solution of Differential and Integral Equations 
SocioEconomic Objective:  E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences 
Funding Details:  
Identification Number or DOI:  10.1016/j.amc.2018.12.015 
URI:  http://eprints.usq.edu.au/id/eprint/36062 
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