Paper Info
Title
A finite difference method for an initial-boundary value problem with a Riemann-Liouville-Caputo spatial fractional derivative.
Abstract
An initial–boundary value problem with a Riemann–Liouville–Caputo space fractional derivative of order α∈(1,2) is considered, where the boundary conditions are reflecting. A fractional Friedrichs’ inequality is derived and is used to prove that the problem approaches a steady-state solution when the source term is zero. The solution of the general problem is approximated using a finite difference scheme defined on a uniform mesh and the error analysis is given in detail for typical solutions which have a weak singularity near the spatial boundary x=0. It is proved that the scheme converges with first order in the maximum norm. Numerical results are given that corroborate our theoretical results for the order of convergence of the difference scheme, the approach of the solution to steady state, and mass conservation.
Year
DOI
Venue
2021
10.1016/j.cam.2020.113020
Journal of Computational and Applied Mathematics
Keywords
DocType
Volume
Fractional differential equation,Time-dependent problem,Riemann–Liouville–Caputo fractional derivative,Weak singularity,Discrete comparison principle,Steady-state problem
Journal
381
ISSN
Citations 
PageRank 
0377-0427
0
0.34
References 
Authors
0
2
Name
Order
Citations
PageRank
J. L. Gracia113918.36
Martin Stynes227357.87