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.
