High-order algorithms for Riesz derivative and their applications (II)
In this paper, we firstly develop two high-order approximate formulas for the Riesz fractional derivative. Secondly, we propose a temporal second order numerical method for a fractional reaction-dispersion equation, where we discretize the Riesz fractional derivative by using two numerical schemes....
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| Veröffentlicht in: | Journal of computational physics 2015-07, Vol.293, p.218-237 |
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| creator | Ding, Hengfei Li, Changpin Chen, YangQuan |
| description | In this paper, we firstly develop two high-order approximate formulas for the Riesz fractional derivative. Secondly, we propose a temporal second order numerical method for a fractional reaction-dispersion equation, where we discretize the Riesz fractional derivative by using two numerical schemes. We prove that the numerical methods for a spatial Riesz fractional reaction dispersion equation are both unconditionally stable and convergent, and the orders of convergence are O([tau] super(2) + h super(6)) and O([tau] super(2) + h super(8)), in which r and h are spatial and temporal step sizes, respectively. Finally, we test our numerical schemes and observe that the numerical results are in good agreement with the theoretical analysis. |
| doi_str_mv | 10.1016/j.jcp.2014.06.007 |
| format | Article |
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| ispartof | Journal of computational physics, 2015-07, Vol.293, p.218-237 |
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| subjects | Approximation Convergence Derivatives Dispersions Mathematical analysis Mathematical models Numerical analysis Temporal logic |
| title | High-order algorithms for Riesz derivative and their applications (II) |
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