In this paper, we present and analyze a fully discrete numerical method for solving the time-fractional diffusion wave equation: ∂<sup>β</sup><sub>t</sub>u - div(a∇u) = f, 1 < β < 2. We first c...
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https://www.riss.kr/link?id=A107603525
2021
English
SCIE,SCOPUS,KCI등재
학술저널
553-569(17쪽)
0
상세조회0
다운로드다국어 초록 (Multilingual Abstract)
In this paper, we present and analyze a fully discrete numerical method for solving the time-fractional diffusion wave equation: ∂<sup>β</sup><sub>t</sub>u - div(a∇u) = f, 1 < β < 2. We first c...
In this paper, we present and analyze a fully discrete numerical method for solving the time-fractional diffusion wave equation: ∂<sup>β</sup><sub>t</sub>u - div(a∇u) = f, 1 < β < 2. We first construct a difference formula to approximate ∂<sup>β</sup><sub>t</sub>u by using an interpolation of derivative type. The truncation error of this formula is of O(△t<sup>2+δ-β</sup>)-order if function u(t) ∈ C<sup>2,δ</sup>[0, T] where 0 ≤ δ ≤ 1 is the Hölder continuity index. This error order can come up to O(△t<sup>3-β</sup>) if u(t) ∈ C<sup>3</sup> [0, T]. Then, in combinination with the linear finite volume discretization on spatial domain, we give a fully discrete scheme for the fractional wave equation. We prove that the fully discrete scheme is unconditionally stable and the discrete solution admits the optimal error estimates in the H<sup>1</sup>-norm and L<sub>2</sub>-norm, respectively. Numerical examples are provided to verify the effectiveness of the proposed numerical method.
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