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Stability analysis of spline collocation methods for fractional differential equations

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  • Cardone, Angelamaria
  • Conte, Dajana

Abstract

This paper deals with spline collocation methods for fractional differential equations, introduced by Pedas and Tamme (2014). Some practical formulas are derived, for the computation of fractional integrals involved in the method, useful for implementation. Linear stability analysis is carried out and stability regions of several methods are provided. Numerical experiments on linear and nonlinear test problems confirm theoretical expectations.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:178:y:2020:i:c:p:501-514
    DOI: 10.1016/j.matcom.2020.07.004
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    References listed on IDEAS

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    1. Cipian Necula, 2008. "Option Pricing in a Fractional Brownian Motion Environment," Advances in Economic and Financial Research - DOFIN Working Paper Series 2, Bucharest University of Economics, Center for Advanced Research in Finance and Banking - CARFIB.
    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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    Cited by:

    1. Li, Yuyu & Wang, Tongke & Gao, Guang-hua, 2023. "The asymptotic solutions of two-term linear fractional differential equations via Laplace transform," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 211(C), pages 394-412.

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