Abstract In the current paper, for the time fractional diffusion equation with an exponential tempering, we propose a numerical algorithm based on the Lagrange-quadratic spline interpolations and the optimal technique. The discretized linear systems and some properties are investigated in details. By using these properties, the coefficient matrix and the right-hand term at each time step are given to analyze the computational cost. Theoretical analyses show that this proposed method enjoys both stability and convergence order of O ( τ 2 + h 4 ) . Some numerical examples are provided to verify the practical feasibility and efficiency of the proposed scheme.

中文翻译：

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时间回火分数阶扩散方程的拉格朗日-二次样条优化配置方法

摘要 在本文中，针对指数回火的时间分数阶扩散方程，我们提出了一种基于拉格朗日-二次样条插值和最优技术的数值算法。详细研究了离散化的线性系统和一些性质。通过使用这些属性，给出每个时间步的系数矩阵和右手项来分析计算成本。理论分析表明，该方法兼具稳定性和收敛阶数为O(τ2+h4)。提供了一些数值例子来验证所提出方案的实际可行性和效率。