Abstract We mainly focus on developing a reduced-order extrapolated finite difference iterative (ROEFDI) method for the Riemann-Liouville tempered fractional derivative (RLTFD) equation. For this reason, we firstly establish a finite difference iterative (FDI) scheme in matrix-form for the RLTFD equation and provide the stability and errors for the FDI solutions. We then develop the ROEFDI method with a few unknowns at each iterative level for the RLTFD equation by means of a proper orthogonal decomposition (POD) and analyze the stability and errors for the ROEFDI solutions by means of matrix approaches, resulting that the theoretical analysis in this paper is very laconic. We finally provide some of numerical tests to confirm the validity of the ROEFDI method for solving the RLTFD equation.

中文翻译：

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黎曼-刘维尔调和分数阶微分方程的一种降阶外推有限差分迭代法

摘要 我们主要致力于为黎曼-刘维尔调和分数阶导数 (RLTFD) 方程开发一种降阶外推有限差分迭代 (ROEFDI) 方法。为此，我们首先为 RLTFD 方程建立矩阵形式的有限差分迭代 (FDI) 方案，并为 FDI 解提供稳定性和误差。然后，我们通过适当的正交分解 (POD) 为 RLTFD 方程开发在每个迭代级别具有一些未知数的 ROEFDI 方法，并通过矩阵方法分析 ROEFDI 解的稳定性和误差，从而得出理论分析这篇论文非常简洁。我们最后提供了一些数值测试来证实 ROEFDI 方法求解 RLTFD 方程的有效性。