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, consis- tency, convergence, and stability analysis of the suggested method are discussed. In this framework, compact struc- tures 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, computa- tional cost and accuracy in comparing with the existing ones in open literature
