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Journal of Scientific Computing

Erschienen in:

17.09.2018

The Temporal Second Order Difference Schemes Based on the Interpolation Approximation for the Time Multi-term Fractional Wave Equation

verfasst von: Hong Sun, Xuan Zhao, Zhi-zhong Sun

Erschienen in: Journal of Scientific Computing | Ausgabe 1/2019

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Abstract

In this paper, two temporal second-order schemes are derived and analyzed for the time multi-term fractional diffusion-wave equation based on the order reduction technique. The weighted average at two time levels is applied to the discretization of the spatial derivative, in which the weight coefficient corresponds to the optimal point for the time discretization. The two difference schemes are proved to be uniquely solvable. The stability and convergence are rigorously investigated utilizing the energy method. In addition, a fast difference scheme is also presented. The applicability and the accuracy of the schemes are demonstrated by several numerical experiments.

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Titel: The Temporal Second Order Difference Schemes Based on the Interpolation Approximation for the Time Multi-term Fractional Wave Equation
verfasst von: Hong Sun
Xuan Zhao
Zhi-zhong Sun
Publikationsdatum: 17.09.2018
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 1/2019
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-018-0820-9

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