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Error Analysis of Nonlinear Time Fractional Mobile/Immobile Advection-Diffusion Equation with Weakly Singular Solutions

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Abstract

In this paper, a weighted and shifted Grünwald-Letnikov difference (WSGD) Legendre spectral method is proposed to solve the two-dimensional nonlinear time fractional mobile/immobile advection-dispersion equation. We introduce the correction method to deal with the singularity in time, and the stability and convergence analysis are proven. In the numerical implementation, a fast method is applied based on a globally uniform approximation of the trapezoidal rule for the integral on the real line to decrease the memory requirement and computational cost. The memory requirement and computational cost are O(Q) and O(QK), respectively, where K is the number of the final time step and Q is the number of quadrature points used in the trapezoidal rule. Some numerical experiments are given to confirm our theoretical analysis and the effectiveness of the presented methods.

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Authors and Affiliations

  1. School of Mathematics, Shandong University **an, 250100, **an, PR China

    Hui Zhang

  2. School of Mathematics, Shandong University, **an, 250100, PR China

    **aoyun Jiang

  3. School of Mathematical Sciences, Queensland University of Technology (QUT), Brisbane, QLD 4001, Australia

    Fawang Liu

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  1. Hui Zhang
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  2. **aoyun Jiang
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  3. Fawang Liu
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Correspondence to **aoyun Jiang.

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Zhang, H., Jiang, X. & Liu, F. Error Analysis of Nonlinear Time Fractional Mobile/Immobile Advection-Diffusion Equation with Weakly Singular Solutions. Fract Calc Appl Anal 24, 202–224 (2021). https://doi.org/10.1515/fca-2021-0009

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  • DOI: https://doi.org/10.1515/fca-2021-0009

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