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A new finite-difference predictor-corrector method for fractional differential equations

Author

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  • Jhinga, Aman
  • Daftardar-Gejji, Varsha

Abstract

We present a new finite-difference predictor-corrector method (L1 - PCM) to solve nonlinear fractional differential equations (FDEs) along with its error and stability analysis. The method is further extended for systems of FDEs. The proposed method is applied to fractional version of chaotic system introduced by Bhalekar and Daftardar-Gejji to explore its rich dynamics. The proposed method is accurate, time-efficient and performs well even for very small values of the order of the derivatives.

Suggested Citation

  • Jhinga, Aman & Daftardar-Gejji, Varsha, 2018. "A new finite-difference predictor-corrector method for fractional differential equations," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 418-432.
    • Handle: RePEc:eee:apmaco:v:336:y:2018:i:c:p:418-432
    DOI: 10.1016/j.amc.2018.05.003
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    Cited by:

    1. Che, Han & Wang, Yu-Lan & Li, Zhi-Yuan, 2022. "Novel patterns in a class of fractional reaction–diffusion models with the Riesz fractional derivative," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 202(C), pages 149-163.
    2. Kumar, Manoj & Daftardar-Gejji, Varsha, 2019. "A new family of predictor-corrector methods for solving fractional differential equations," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
    3. Sivalingam, S M & Kumar, Pushpendra & Trinh, Hieu & Govindaraj, V., 2024. "A novel L1-Predictor-Corrector method for the numerical solution of the generalized-Caputo type fractional differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 220(C), pages 462-480.
    4. Lin Zhu, 2019. "A Second-Order Uniformly Stable Explicit Asymmetric Discretization Method for One-Dimensional Fractional Diffusion Equations," Complexity, Hindawi, vol. 2019, pages 1-12, May.

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