A spectrally accurate step-by-step method for the numerical solution of fractional differential equations
Numerical Analysis
2024-04-09 v2 Numerical Analysis
Abstract
In this paper we consider the numerical solution of fractional differential equations. In particular, we study a step-by-step graded mesh procedure based on an expansion of the vector field using orthonormal Jacobi polynomials. Under mild hypotheses, the proposed procedure is capable of getting spectral accuracy. A few numerical examples are reported to confirm the theoretical findings.
Keywords
Cite
@article{arxiv.2310.10526,
title = {A spectrally accurate step-by-step method for the numerical solution of fractional differential equations},
author = {L. Brugnano and K. Burrage and P. Burrage and F. Iavernaro},
journal= {arXiv preprint arXiv:2310.10526},
year = {2024}
}
Comments
26 pages, 2 figures, 7 tables, a few typos fixed in the updated version