The high-order compact numerical algorithms for the two-dimensional fractional sub-diffusion equation

Cui-cui Ji and Zhi-zhong Sun

Applied Mathematics and Computation, 2015, vol. 269, issue C, 775-791

Abstract: In this paper, performing the average operators on the space variables, a numerical scheme with third-order temporal convergence for the two-dimensional fractional sub-diffusion equation is considered, for which the unconditional stability and convergence in L1(L∞)-norm are strictly analyzed for α ∈ (0, 0.9569347] by using the discrete energy method. Therewith, adding small perturbation terms, we construct a compact alternating direction implicit difference scheme for the two-dimensional case. Finally, some numerical results have been given to show the computational efficiency and numerical accuracy of both schemes for all α ∈ (0, 1).

Keywords: Two-dimensional fractional sub-diffusion equation; Numerical schemes; High-order; Discrete energy method; Stability; Convergence (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:269:y:2015:i:c:p:775-791

DOI: 10.1016/j.amc.2015.07.088

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