This study presents a robust modification of Chebyshev ϑ‐weighted Crank–Nicolson method for analyzing the sub‐diffusion equations in the Caputo fractional sense. In order to solve the problem, by discretization of the sub‐fractional diffusion equations using Taylor's expansion a linear system of algebraic equations that can be analyzed by numerical methods is presented. Furthermore, consistency, convergence, and stability analysis of the suggested method are discussed. In this framework, compact structures of sub‐diffusion equations are considered as prototype examples. The main advantage of the proposed method is that, it is more efficient in terms of CPU time, computational cost and accuracy in comparing with the existing ones in open literature.

中文翻译：

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修正的Chebyshev ϑ加权Crank-Nicolson方法用于分析分数次扩散方程

这项研究提出了Chebyshev ϑ加权Crank-Nicolson方法的稳健修改，用于分析Caputo分数意义上的子扩散方程。为了解决该问题，通过使用泰勒展开式对次分数阶扩散方程进行离散化，提出了可以通过数值方法进行分析的线性代数方程组。此外，讨论了所建议方法的一致性，收敛性和稳定性分析。在此框架中，子扩散方程的紧凑结构被视为原型示例。所提出的方法的主要优点是，与公开文献中的现有方法相比，它在CPU时间，计算成本和准确性方面更为有效。