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Correction of a High-Order Numerical Method for Approximating Time-Fractional Wave Equation
Ramezani, Mohadese Mokhtari, Reza Yan, Yubin
Ramezani, Mohadese
Mokhtari, Reza
Yan, Yubin
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2024-07-22
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Abstract
A high-order time discretization scheme to approximate the time-fractional wave equation with the Caputo fractional derivative of order $\alpha \in (1, 2)$ is studied. We establish a high-order formula for approximating the Caputo fractional derivative of order $\alpha \in (1, 2)$. Based on this approximation, we propose a novel numerical method to solve the time-fractional wave equation. Remarkably, this method corrects only one starting step and demonstrates second-order convergence in both homogeneous and inhomogeneous cases, regardless of whether the data is smooth or nonsmooth. We also analyze the stability region associated with the proposed numerical method. Some numerical examples are given to elucidate the convergence analysis.
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Ramezani, M., Mokhtari, R., & Yan, Y. (2024). Correction of a high-order numerical method for approximating time-fractional wave equation. Journal of Scientific Computing, 100, 71. https://doi.org/10.1007/s10915-024-02625-y
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Springer
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Journal of Scientific Computing
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Article
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This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s10915-024-02625-y
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0885-7474
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1573-7691
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