A shooting-Newton procedure for solving fractional terminal value problems

Luigi Brugnano, Gianmarco Gurioli and Felice Iavernaro

Applied Mathematics and Computation, 2025, vol. 489, issue C

Abstract: In this paper we consider the numerical solution of fractional terminal value problems: namely, terminal value problems for fractional differential equations. In particular, the proposed method 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, i.e., initial value problems for fractional differential equations. As a result, the method is able to produce spectrally accurate solutions of fractional terminal value problems. Some numerical tests are reported to make evidence of its effectiveness.

Keywords: Fractional differential equations; Fractional integrals; Terminal value problems; Jacobi polynomials; Fractional Hamiltonian Boundary Value Methods; FHBVMs (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:489:y:2025:i:c:s0096300324006258

DOI: 10.1016/j.amc.2024.129164

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