Jin, B;
Ito, K;
Takeuchi, T;
(2015)
On a Legendre tau method for boundary value problems with a Caputo derivative.
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Abstract
In this paper, we revisit a Legendre-tau method for two-point boundary value problems with a Caputo fractional derivative in the leading term, and establish an L2 error estimate for smooth solutions. Further, we apply the method to the Sturm-Liouville problem. Numerical experiments indi- cate that for the source problem, it converges steadily at an algebraic rate even for nonsmooth data, and the convergence rate enhances with problem data regularity, whereas for the Sturm-Liouville problem, it always yields excellent convergence for eigenvalue approximations.
| Type: | Working / discussion paper |
|---|---|
| Title: | On a Legendre tau method for boundary value problems with a Caputo derivative |
| Open access status: | An open access version is available from UCL Discovery |
| Language: | English |
| Keywords: | Caputo fractional derivative, Legendre tau method, error estimates, eigenvalue approximation |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1470735 |
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