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<p>This paper introduces a high-order compact finite difference method for convection-reaction–subdiffusion equation with variable exponent and coefficients. To account for the difficulties caused by the non-positivity and non-monotonicity of the variable-exponent power-law kernel and the convection term, a space-time transformation is adopted to reformulate the original problem to a more tractable Volterra integrodifferential model. The interpolation quadrature rule is used to approximate the memory terms, and the spatial discretization is performed using the compact difference method. Stability and convergence of the scheme are rigorously proved and substantiated by numerical experiments.</p>

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High-order compact difference method for convection-reaction–subdiffusion equation with variable exponent and coefficients

  • 期刊论文

  • 发表日期：

    2025年4月1日

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  • Mengmeng Liu,
  • Xiangcheng Zheng,
  • Kexin Li,
  • Wenlin Qiu

摘要

This paper introduces a high-order compact finite difference method for convection-reaction–subdiffusion equation with variable exponent and coefficients. To account for the difficulties caused by the non-positivity and non-monotonicity of the variable-exponent power-law kernel and the convection term, a space-time transformation is adopted to reformulate the original problem to a more tractable Volterra integrodifferential model. The interpolation quadrature rule is used to approximate the memory terms, and the spatial discretization is performed using the compact difference method. Stability and convergence of the scheme are rigorously proved and substantiated by numerical experiments.