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首页> 外文期刊>Journal of Scientific Computing >A High-Order Algorithm for Time-Caputo-Tempered Partial Differential Equation with Riesz Derivatives in Two Spatial Dimensions
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A High-Order Algorithm for Time-Caputo-Tempered Partial Differential Equation with Riesz Derivatives in Two Spatial Dimensions

机译：具有二维空间Riesz导数的时容调和偏微分方程的高阶算法

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摘要

A novel second-order numerical approximation for the Riemann-Liouville tempered fractional derivative, called the tempered fractional-compact difference formula is derived by using the tempered Grunwald difference operator and its asymptotic expansion. Using the relationship between Riemann-Liouville and the Caputo tempered fractional derivatives, then the constructed approximation formula is applied to deal with the time-Caputo-tempered partial differential equation in time, while the spatial Riesz derivative are discretized by the fourth-order compact numerical differential formulas. By using the energy method, it is proved that the proposed algorithm to be unconditionally stable and convergent with order where is the temporal stepsize and h1,h2 are the spatial stepsizes respectively. Finally, some numerical examples are performed to testify the effectiveness of the obtained algorithm.
机译：通过使用回火的Grunwald差分算子及其渐近展开，推导了黎曼-柳维尔回火的分数阶导数的新型二阶数值近似，称为回火的分数-紧凑差分公式。利用Riemann-Liouville和Caputo回火的分数阶导数之间的关系，构造的近似公式可以及时处理时间-Caputo回火的偏微分方程，而空间Riesz导数则通过四阶紧致数值离散化微分公式。通过能量方法，证明了该算法是无条件稳定的，并且收敛于阶，其中时间步长为h1，h2为空间步长。最后，通过数值例子验证了所提算法的有效性。

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