@article{Lu2026, 
author = {Lingna Lu and Changshun Hou},
title = {Analysis and numerical implementation of high-order method for distributed-order diffusion model},
year = {2026},
journal = {Networks and Heterogeneous Media},
volume = {21},
number = {1},
pages = {261-275},
keywords = {diffusion model, fractional derivative, convergence, stability},
url = {https://www.sciopen.com/article/10.3934/nhm.2026013},
doi = {10.3934/nhm.2026013},
abstract = {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  →  ∞. 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.}
}