In this manuscript, we study a generalized fractional reaction-diffusion model involving a distributed-order operator. An efficient hybrid approach is proposed to solve the presented model. The L1 approximation is utilized to discretize the time variable, while the mixed finite element method is employed for spatial discretization. A detailed error and stability analysis of the proposed method is provided. Furthermore, we prove that the computational accuracy achieved by the proposed approach is of order O(h2+(Δt)3−ξmax). To validate and evaluate the numerical approach, three numerical experiments are conducted, with results presented through graphs and tables.

中文翻译：

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求解广义分数级反应-扩散模型的有效数值方法研究，涉及分布阶算子和稳定性分析


在这份手稿中，我们研究了一个涉及分布式阶算子的广义分数级反应扩散模型。提出了一种高效的混合方法来求解所提出的模型。L1 近似用于离散时间变量，而混合有限元方法用于空间离散化。对所提方法进行了详细的误差和稳定性分析。此外，我们证明所提出的方法所达到的计算精度为 O（h2+（Δt）3−ξmax）。为了验证和评估数值方法，进行了三个数值实验，结果通过图形和表格表示。