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Jacobi-Davidson method for the second order fractional eigenvalue problems

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  • He, Ying
  • Zuo, Qian

Abstract

We present a Jacobi-Davidson method for solving the second order fractional eigenvalue problems by using the finite difference formulas of the Caputo fractional derivatives. In order to speed up the convergence of the method, we propose the preconditioned generalized minimal residuals method (PGMRES) to solve the correction equation and analyze the spectral clustering property of the preconditioned matrix. Numerical results show that the Jacobi-Davidson method is efficient for solving the fractional eigenvalue problems.

Suggested Citation

  • He, Ying & Zuo, Qian, 2021. "Jacobi-Davidson method for the second order fractional eigenvalue problems," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    • Handle: RePEc:eee:chsofr:v:143:y:2021:i:c:s0960077920310055
    DOI: 10.1016/j.chaos.2020.110614
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    References listed on IDEAS

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    1. Al-Mdallal, Qasem M., 2009. "An efficient method for solving fractional Sturm–Liouville problems," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 183-189.
    2. Duan, Jun-Sheng & Wang, Zhong & Liu, Yu-Lu & Qiu, Xiang, 2013. "Eigenvalue problems for fractional ordinary differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 46(C), pages 46-53.
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    Cited by:

    1. Gupta, Sandipan & Ranta, Shivani, 2022. "Legendre wavelet based numerical approach for solving a fractional eigenvalue problem," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).

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