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arXiv · 2310.10526

A spectrally accurate step-by-step method for the numerical solution of fractional differential equations

L. Brugnano·K. Burrage·P. Burrage·F. Iavernaro
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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.

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L. Brugnano, K. Burrage, P. Burrage, F. Iavernaro. 2023-12-16. A spectrally accurate step-by-step method for the numerical solution of fractional differential equations. https://doi.org/10.1007/s10915-024-02517-1

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