An alternating segment Crank–Nicolson parallel difference scheme for the time fractional sub-diffusion equation

Abstract

Abstract In this paper, an alternating segment Crank–Nicolson (ASC-N) parallel difference scheme is proposed for the time fractional sub-diffusion equation, which consists of the classical Crank–Nicolson scheme, four kinds of Saul’yev asymmetric schemes, and alternating segment technique. Theoretical analysis reveals that the ASC-N scheme is unconditionally stable and convergent by mathematical induction method. Finally, the theoretical analysis is verified by numerical experiments, which show that the ASC-N scheme is efficient for solving the time fractional sub-diffusion equation.

Keywords

• Time fractional sub-diffusion equation
• Alternating segment Crank–Nicolson scheme
• Stability
• Convergence
• Parallel computing