In this paper we consider the numerical solution of fractional differential equations. In par- ticular, we study a step-by-step procedure, defined over a graded mesh, which is based on a truncated expansion of the vector field along the orthonormal Jacobi polynomial basis. Under mild hypotheses, the proposed procedure is capable of getting spectral accuracy. A few numerical examples are reported to confirm the theoretical findings.
A Spectrally Accurate Step-by-Step Method for the Numerical Solution of Fractional Differential Equations / Brugnano, Luigi; Burrage, Kevin; Burrage, Pamela; Iavernaro, Felice. - In: JOURNAL OF SCIENTIFIC COMPUTING. - ISSN 0885-7474. - STAMPA. - 99:(2024), pp. 48.1-48.28. [10.1007/s10915-024-02517-1]
A Spectrally Accurate Step-by-Step Method for the Numerical Solution of Fractional Differential Equations
Brugnano, Luigi
;
2024
Abstract
In this paper we consider the numerical solution of fractional differential equations. In par- ticular, we study a step-by-step procedure, defined over a graded mesh, which is based on a truncated expansion of the vector field along the orthonormal Jacobi polynomial basis. 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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