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Alternating Segment Explicit-Implicit and Implicit-Explicit Parallel Difference Method for Time Fractional Sub-Diffusion Equation

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Document pages: 17 pages

Abstract: The fractional diffusion equations can accuratelydescribe the migration process of anomalous diffusion, which are widely appliedin the field of natural science and engineering calculations. This paperproposed a kind of numerical methods with parallel nature which were thealternating segment explicit-implicit (ASE-I) and implicit-explicit (ASI-E)difference method for the time fractional sub-diffusion equation. It is basedon the combination of the explicit scheme, implicit scheme, improved Saul’yevasymmetric scheme and the alternating segment technique. Theoretical analyseshave shown that the solution of ASE-I (ASI-E) scheme is uniquely solvable. Atthe same time the stability and convergence of the two schemes were proved bythe mathematical induction. The theoretical analyses are verified by numericalexperiments. Meanwhile the ASE-I (ASI-E) scheme has the higher computationalefficiency compared with the implicit scheme. Therefore it is feasible to usethe parallel difference schemes for solving the time fractional diffusionequation.

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