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A high-order scheme to approximate the Caputo fractional derivative and its application to solve the fractional diffusion wave equation
Du, Ruilian Yan, Yubin Liang, Zongqi
Du, Ruilian
Yan, Yubin
Liang, Zongqi
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2018-10-05
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Abstract
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. 1312-1330
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Elsevier
Journal
Journal of Computational Physics
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DOI
10.1016/j.jcp.2018.10.011
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PubMed Central ID
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Article
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en
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0021-9991