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Unconditionally stable and convergent difference scheme for superdiffusion with extrapolation
Yan, Yubin Yang, Jinping Pani, Amiya Green, Charles
Yan, Yubin
Yang, Jinping
Pani, Amiya
Green, Charles
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2023-11-23
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Abstract
Approximating the Hadamard finite-part integral by the quadratic interpolation polynomials, we obtain a scheme for approximating the Riemann-Liouville fractional derivative of order α∈(1, 2) and the error is shown to have the asymptotic expansion (d3τ3-α+d4τ4-α+d5τ5-α+⋯)+(d2∗τ4+d3∗τ6+d4∗τ8+⋯) at any fixed time, where τ denotes the step size and dl, l=3, 4, ⋯ and dl∗, l=2, 3, ⋯ are some suitable constants. Applying the proposed scheme in temporal direction and the central difference scheme in spatial direction, a new finite difference method is developed for approximating the time fractional wave equation. The proposed method is unconditionally stable, convergent with order O(τ3-α), α∈(1, 2) and the error has the asymptotic expansion. Richardson extrapolation is applied to improve the accuracy of the numerical method. The convergence orders are O(τ4-α) and O(τ2(3-α)), α∈(1, 2), respectively, after first two extrapolations. Numerical examples are presented to show that the numerical results are consistent with the theoretical findings.
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Yang, J., Green, C., Pani, A. K., & Yan, Y. (2024). Unconditionally stable and convergent difference scheme for superdiffusion with extrapolation. Journal of Scientific Computing, 98(1), article-number 12. https://doi.org/10.1007/s10915-023-02395-z
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Springer
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Journal of Scientific Computing
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Article
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The version of record of this article, first published in [Journal of Scientific Computing], is available online at Publisher’s website: https://doi.org/10.1007/s10915-023-02395-z
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0885-7474
EISSN
1573-7691