TITLE:
Alternating Segment Explicit-Implicit and Implicit-Explicit Parallel Difference Method for Time Fractional Sub-Diffusion Equation
AUTHORS:
Lifei Wu, Yadi Zhao, Xiaozhong Yang
KEYWORDS:
Time Fractional Diffusion Equation, ASE-I, ASI-E, Stability, Parallel Computing
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.6 No.5,
May
28,
2018
ABSTRACT: The fractional diffusion equations can accurately
describe the migration process of anomalous diffusion, which are widely applied
in the field of natural science and engineering calculations. This paper
proposed a kind of numerical methods with parallel nature which were the
alternating segment explicit-implicit (ASE-I) and implicit-explicit (ASI-E)
difference method for the time fractional sub-diffusion equation. It is based
on the combination of the explicit scheme, implicit scheme, improved Saul’yev
asymmetric scheme and the alternating segment technique. Theoretical analyses
have shown that the solution of ASE-I (ASI-E) scheme is uniquely solvable. At
the same time the stability and convergence of the two schemes were proved by
the mathematical induction. The theoretical analyses are verified by numerical
experiments. Meanwhile the ASE-I (ASI-E) scheme has the higher computational
efficiency compared with the implicit scheme. Therefore it is feasible to use
the parallel difference schemes for solving the time fractional diffusion
equation.