A shooting-Newton procedure for solving fractional terminal value problems

In this paper we consider the numerical solution of fractional terminal value problems (FDE-TVPs). In particular, the proposed procedure uses a Newton-type iteration which is particularly efficient when coupled with a recently-introduced step-by-step procedure for solving fractional initial value pr...

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Bibliographic Details
Published in:arXiv.org 2024-10
Main Authors: Brugnano, Luigi, Gurioli, Gianmarco, Iavernaro, Felice
Format: Article
Language:English
Subjects:
Boundary value problems
Iterative methods
Online Access:Get full text
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Summary:In this paper we consider the numerical solution of fractional terminal value problems (FDE-TVPs). In particular, the proposed procedure uses a Newton-type iteration which is particularly efficient when coupled with a recently-introduced step-by-step procedure for solving fractional initial value problems (FDE-IVPs), able to produce spectrally accurate solutions of FDE problems. Some numerical tests are reported to make evidence of its effectiveness.
ISSN:2331-8422
DOI:10.48550/arxiv.2312.08516