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In this article, the modified wavenumbers for several numerical approximations of the Caputo fractional derivatives based on the Lagrange interpolation method over a uniform mesh are derived. With regard to the modified wavenumbers, the Fourier analysis of differencing errors is performed to quantify the resolution characteristics of these approximations. The plots of original wave numbers against modified wave numbers are presented for each approximation method. Numerical experiments over a test case are performed to validate the accuracy and efficiency of different approximation schemes for the Caputo fractional derivative.

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Fourier Error Analysis of Caputo Derivative Approximations Based on Lagrange Interpolation over Uniform Mesh

  • 会议论文

  • 发表日期：

    2025年

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  • Shweta Kumari,
  • Mani Mehra

摘要

In this article, the modified wavenumbers for several numerical approximations of the Caputo fractional derivatives based on the Lagrange interpolation method over a uniform mesh are derived. With regard to the modified wavenumbers, the Fourier analysis of differencing errors is performed to quantify the resolution characteristics of these approximations. The plots of original wave numbers against modified wave numbers are presented for each approximation method. Numerical experiments over a test case are performed to validate the accuracy and efficiency of different approximation schemes for the Caputo fractional derivative.