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Networks and Heterogeneous Media

2026, Volume 21, Issue 1: 261-275. doi: 10.3934/nhm.2026013
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Analysis and numerical implementation of high-order method for distributed-order diffusion model

  • 1.
    School of Basic Sciences, Zhengzhou University of Technology, Zhengzhou 450044, China
  • 2.
    School of Mathematics and Statistics, Henan University of Technology, Zhengzhou 450001, China
  • Published: 10 March 2026

  • This work proposes a high-order discontinuous Galerkin (DG) formulation employing generalized alternating numerical fluxes for approximating solutions to the distributed-order diffusion equation. Such models often arise in ultraslow diffusion, where solutions decay only logarithmically as $ t \to \infty $. Utilizing the Grünwald–Letnikov scheme and the DG method, we construct a fully discrete numerical algorithm. Using a rigorous induction argument, we prove unconditional stability and convergence of the proposed scheme. A comprehensive set of computational experiments is presented to validate the efficacy and performance of the method.

    Citation: Lingna Lu, Changshun Hou. Analysis and numerical implementation of high-order method for distributed-order diffusion model[J]. Networks and Heterogeneous Media, 2026, 21(1): 261-275. doi: 10.3934/nhm.2026013

    Related Papers:

  • This work proposes a high-order discontinuous Galerkin (DG) formulation employing generalized alternating numerical fluxes for approximating solutions to the distributed-order diffusion equation. Such models often arise in ultraslow diffusion, where solutions decay only logarithmically as $ t \to \infty $. Utilizing the Grünwald–Letnikov scheme and the DG method, we construct a fully discrete numerical algorithm. Using a rigorous induction argument, we prove unconditional stability and convergence of the proposed scheme. A comprehensive set of computational experiments is presented to validate the efficacy and performance of the method.



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