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Finite difference/spectral-Galerkin method for a two-dimensional distributed-order time–space fractional reaction–diffusion equation.
- Source :
-
Applied Mathematics Letters . Nov2018, Vol. 85, p157-163. 7p. - Publication Year :
- 2018
-
Abstract
- In this letter, we consider the numerical approximation of a two-dimensional distributed-order time–space fractional reaction–diffusion equation. The time- and space-fractional derivatives are considered in the senses of Caputo and Riesz, respectively. By using the composite mid-point quadrature, the original fractional problem is approximated by a multi-term time–space fractional differential equation. Then the multi-term Caputo fractional derivatives are discretized by the L 2 - 1 σ formula. We apply the Legendre–Galerkin spectral method for the spatial approximation. Two numerical experiments with smooth and non-smooth initial conditions, respectively, are performed to illustrate the robustness of the proposed method. The results show that: our scheme can arrive at the spectral accuracy (resp. algebraic accuracy) in space for the problem with smooth (resp. non-smooth) initial condition. For both of these two cases, our scheme can lead to the second-order accuracies in time. Additionally, the convergence rates in both spatial and temporal distributed-order variables are two. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 08939659
- Volume :
- 85
- Database :
- Academic Search Index
- Journal :
- Applied Mathematics Letters
- Publication Type :
- Academic Journal
- Accession number :
- 130419767
- Full Text :
- https://doi.org/10.1016/j.aml.2018.06.005