Trapezoidal methods for fractional differential equations: Theoretical and computational aspects
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DOI: 10.1016/j.matcom.2013.09.012
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References listed on IDEAS
- Galeone, Luciano & Garrappa, Roberto, 2008. "Fractional Adams–Moulton methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(4), pages 1358-1367.
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Cited by:
- Cardone, Angelamaria & Conte, Dajana, 2020. "Stability analysis of spline collocation methods for fractional differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 178(C), pages 501-514.
- Marina Popolizio, 2018. "Numerical Solution of Multiterm Fractional Differential Equations Using the Matrix Mittag–Leffler Functions," Mathematics, MDPI, vol. 6(1), pages 1-13, January.
- Das, Saptarshi & Pan, Indranil & Das, Shantanu, 2016. "Effect of random parameter switching on commensurate fractional order chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 157-173.
- Roberto Garrappa, 2018. "Numerical Solution of Fractional Differential Equations: A Survey and a Software Tutorial," Mathematics, MDPI, vol. 6(2), pages 1-23, January.
- Rainey Lyons & Aghalaya S. Vatsala & Ross A. Chiquet, 2017. "Picard’s Iterative Method for Caputo Fractional Differential Equations with Numerical Results," Mathematics, MDPI, vol. 5(4), pages 1-9, November.
- Kai Diethelm & Roberto Garrappa & Martin Stynes, 2020. "Good (and Not So Good) Practices in Computational Methods for Fractional Calculus," Mathematics, MDPI, vol. 8(3), pages 1-21, March.
- Hamdan, Nur ’Izzati & Kilicman, Adem, 2018. "A fractional order SIR epidemic model for dengue transmission," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 55-62.
- Moustafa, Mahmoud & Mohd, Mohd Hafiz & Ismail, Ahmad Izani & Abdullah, Farah Aini, 2018. "Dynamical analysis of a fractional-order Rosenzweig–MacArthur model incorporating a prey refuge," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 1-13.
- Čermák, Jan & Nechvátal, Luděk, 2019. "Stability and chaos in the fractional Chen system," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 24-33.
- Dmytro Sytnyk & Barbara Wohlmuth, 2023. "Exponentially Convergent Numerical Method for Abstract Cauchy Problem with Fractional Derivative of Caputo Type," Mathematics, MDPI, vol. 11(10), pages 1-35, May.
- Yang, Changqing, 2023. "Improved spectral deferred correction methods for fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
- Jannelli, Alessandra, 2024. "A finite difference method on quasi-uniform grids for the fractional boundary-layer Blasius flow," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 215(C), pages 382-398.
- Bonab, Zahra Farzaneh & Javidi, Mohammad, 2020. "Higher order methods for fractional differential equation based on fractional backward differentiation formula of order three," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 172(C), pages 71-89.
- Sowa, Marcin, 2018. "Application of SubIval in solving initial value problems with fractional derivatives," Applied Mathematics and Computation, Elsevier, vol. 319(C), pages 86-103.
- Arenas, Abraham J. & González-Parra, Gilberto & Chen-Charpentier, Benito M., 2016. "Construction of nonstandard finite difference schemes for the SI and SIR epidemic models of fractional order," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 121(C), pages 48-63.
- Wang, Yuan-Ming & Xie, Bo, 2023. "A fourth-order fractional Adams-type implicit–explicit method for nonlinear fractional ordinary differential equations with weakly singular solutions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 212(C), pages 21-48.
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Keywords
Fractional differential equations; Multistep methods; Trapezoidal method; Stability; Computational aspects;All these keywords.
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