dc.contributor.author Du, Ruilian * dc.contributor.author Yan, Yubin * dc.contributor.author Liang, Zongqi * dc.date.accessioned 2018-10-31T15:39:25Z dc.date.available 2018-10-31T15:39:25Z dc.date.issued 2018-10-05 dc.identifier.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 en dc.identifier.issn 0021-9991 dc.identifier.doi 10.1016/j.jcp.2018.10.011 dc.identifier.uri http://hdl.handle.net/10034/621500 dc.description.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. dc.language.iso en en dc.publisher Elsevier en dc.relation.url https://www.sciencedirect.com/science/article/pii/S0021999118306685 en dc.rights.uri https://creativecommons.org/licenses/by-nc-nd/3.0/ en dc.subject Caputo fractional derivative en dc.subject fractional diffusion wave equation en dc.subject Finite difference method en dc.title A high-order scheme to approximate the Caputo fractional derivative and its application to solve the fractional diffusion wave equation en dc.type Article en dc.contributor.department Jimei University; University of Chester en dc.identifier.journal Journal of Computational Physics dc.date.accepted 2018-10-03 or.grant.openaccess Yes en rioxxterms.funder unfunded en_US rioxxterms.identifier.project unfunded en_US rioxxterms.version AM en rioxxterms.licenseref.startdate 2019-10-05 refterms.dateFCD 2018-10-12T15:19:36Z refterms.versionFCD AM refterms.dateFOA 2019-10-05T00:00:00Z
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