Paper Info
Title
Convergence Outside the Initial Layer for a Numerical Method for the Time-Fractional Heat Equation.
Abstract
In this paper a fractional heat equation is considered; it has a Caputo time-fractional derivative of order delta where 0 < delta < 1. It is solved numerically on a uniform mesh using the classical L1 and standard three-point finite difference approximations for the time and spatial derivatives, respectively. In general the true solution exhibits a layer at the initial time t = 0; this reduces the global order of convergence of the finite difference method to O(h(2) + tau(delta)), where h and tau are the mesh widths in space and time, respectively. A new estimate for the L1 approximation shows that its truncation error is smaller away from t = 0. This motivates us to investigate if the finite difference method is more accurate away from t = 0. Numerical experiments with various non-smooth and incompatible initial conditions show that, away from t = 0, one obtains O(h(2) + tau) convergence.
Year
DOI
Venue
2016
10.1007/978-3-319-57099-0_8
Lecture Notes in Computer Science
Keywords
Field
DocType
Time-fractional heat equation,Caputo fractional derivative,Initial-boundary value problem,L1 scheme,Layer region,Smooth and non-smooth data,Compatibility conditions
Convergence (routing),Order of accuracy,Truncation error,Mathematical analysis,Finite difference,Finite difference method,Rate of convergence,Heat equation,Numerical analysis,Physics
Conference
Volume
ISSN
Citations 
10187
0302-9743
0
PageRank 
References 
Authors
0.34
0
3
Name
Order
Citations
PageRank
J. L. Gracia113918.36
Eugene O'Riordan212019.17
Martin Stynes327357.87