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<p>The fractional Laplacian has been extensively applied to model nonlocal phenomena such as anomalous diffusion. In this paper, we propose to employ the Gegenbauer collocation method to discretize one special case of the fractional Laplacian-Riesz fractional derivative of variable-order (VO). We analyze the features of the collocation method for both constant-order and VO cases and develop an efficient preconditioner. We present some approximation errors and several numerical tests to confirm the efficiency of the method.</p>

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Gegenbauer Collocation Discretization of Riesz Derivative of Variable-Order

  • 期刊论文

  • 发表日期：

    2025年10月3日

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  • Hongjun Ma,
  • Wenbin Li,
  • Tinggang Zhao,
  • Zhongqiang Zhang

摘要

The fractional Laplacian has been extensively applied to model nonlocal phenomena such as anomalous diffusion. In this paper, we propose to employ the Gegenbauer collocation method to discretize one special case of the fractional Laplacian-Riesz fractional derivative of variable-order (VO). We analyze the features of the collocation method for both constant-order and VO cases and develop an efficient preconditioner. We present some approximation errors and several numerical tests to confirm the efficiency of the method.