Advances in Difference Equations (Aug 2018)

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

  • Lifei Wu,
  • Xiaozhong Yang,
  • Yanhua Cao

DOI
https://doi.org/10.1186/s13662-018-1749-x
Journal volume & issue
Vol. 2018, no. 1
pp. 1 – 18

Abstract

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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