A high-order scheme to approximate the Caputo fractional derivative and its application to solve the fractional diffusion wave equation
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Jimei University; University of ChesterPublication Date
2018-10-05
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A new high-order finite difference scheme to approximate the Caputo fractional derivative $\frac{1}{2} \big ( \, _{0}^{C}D^{\alpha}_{t}f(t_{k})+ \, _{0}^{C}D^{\alpha}_{t}f(t_{k-1}) \big ), k=1, 2, \dots, N, $ with the convergence order $O(\Delta t^{4-\alpha}), \, \alpha\in(1,2)$ is obtained when $f^{\prime \prime \prime} (t_{0})=0$, where $\Delta t$ denotes the time step size. Based on this scheme we introduce a finite difference method for solving fractional diffusion wave equation with the convergence order $O(\Delta t^{4-\alpha} + h^2)$, where $h$ denotes the space step size. Numerical examples are given to show that the numerical results are consistent with the theoretical results.Citation
Du, R., Yan, Y. and Liang, Z., (2019). A high-order scheme to approximate the caputo fractional derivative and its application to solve the fractional diffusion wave equation, Journal of Computational Physics, 376, pp. 1312-1330Publisher
ElsevierJournal
Journal of Computational PhysicsAdditional Links
https://www.sciencedirect.com/science/article/pii/S0021999118306685Type
ArticleLanguage
enISSN
0021-9991ae974a485f413a2113503eed53cd6c53
10.1016/j.jcp.2018.10.011
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Except where otherwise noted, this item's license is described as https://creativecommons.org/licenses/by-nc-nd/3.0/