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arXiv · 2511.11082

Numerical approximation of Caputo-type advection-diffusion equations in one and multiple spatial dimensions via shifted Chebyshev polynomials

Francisco de la Hoz·Peru Muniain
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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.

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Francisco de la Hoz, Peru Muniain. 2025-11-14. Numerical approximation of Caputo-type advection-diffusion equations in one and multiple spatial dimensions via shifted Chebyshev polynomials. https://arxiv.org/abs/2511.11082

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