Numerical approximation of Caputo-type advection-diffusion equations in one and multiple spatial dimensions via shifted Chebyshev polynomials
Abstract
In this paper, using a pseudospectral approach, we develop operational matrices based on the shifted Chebyshev polynomials to approximate numerically Caputo fractional derivatives and Riemann-Liouville fractional integrals. In order to make the generation of these matrices stable, we use variable precision arithmetic. Then, we apply the Caputo differentiation matrices to solve numerically Caputo-type advection-diffusion equations in one and multiple spatial dimensions, which involves transforming the discretization of the concerning equation into a Sylvester (tensor) equation. We provide complete Matlab codes, whose implementation is carefully explained. The numerical experiments involving highly oscillatory functions in time confirm the effectiveness of this approach.
Keywords
Cite
@article{arxiv.2511.11082,
title = {Numerical approximation of Caputo-type advection-diffusion equations in one and multiple spatial dimensions via shifted Chebyshev polynomials},
author = {Francisco de la Hoz and Peru Muniain},
journal= {arXiv preprint arXiv:2511.11082},
year = {2025}
}
Comments
23 pages, 3 figures