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A shooting-Newton procedure for solving fractional terminal value problems

Author

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  • Brugnano, Luigi
  • Gurioli, Gianmarco
  • Iavernaro, Felice

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.

Suggested Citation

  • Brugnano, Luigi & Gurioli, Gianmarco & Iavernaro, Felice, 2025. "A shooting-Newton procedure for solving fractional terminal value problems," Applied Mathematics and Computation, Elsevier, vol. 489(C).
    • Handle: RePEc:eee:apmaco:v:489:y:2025:i:c:s0096300324006258
    DOI: 10.1016/j.amc.2024.129164
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    References listed on IDEAS

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    1. Roberto Garrappa, 2018. "Numerical Solution of Fractional Differential Equations: A Survey and a Software Tutorial," Mathematics, MDPI, vol. 6(2), pages 1-23, January.
    2. Garrappa, Roberto, 2015. "Trapezoidal methods for fractional differential equations: Theoretical and computational aspects," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 110(C), pages 96-112.
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