Second-Order Stable Finite Difference Schemes for the Time-Fractional Diffusion-Wave Equation
Second-Order Stable Finite Difference Schemes for the Time-Fractional Diffusion-Wave Equation
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DOI：
10.1007/s10915-014-9966-2
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发表时间：
2014-07
影响因子：
2.5
通讯作者：
Fanhai Zeng
中科院分区：
文献类型：
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作者：
Fanhai Zeng
对时间分数阶扩散波动方程提出了两个稳定的二阶差分格式和一个条件稳定的二阶差分格式。在第一个方案中，我们在时间上应用分数梯形法则，在空间上应用中心差分。第二种方案采用广义Newton-Gregory公式，第三种方案采用修正的Newton-Gregory公式。第二个方案是条件稳定的，而第一个和第三个方案是稳定的。我们应用的方法考虑方程也线性对流反应项，并获得二阶计划在时间和空间。数值算例与已有算法的比较验证了理论分析的正确性，并表明新算法具有更好的性能.
We propose two stable and one conditionally stable finite difference schemes of second-order in both time and space for the time-fractional diffusion-wave equation. In the first scheme, we apply the fractional trapezoidal rule in time and the central difference in space. We use the generalized Newton–Gregory formula in time for the second scheme and its modification for the third scheme. While the second scheme is conditionally stable, the first and the third schemes are stable. We apply the methodology to the considered equation with also linear advection–reaction terms and also obtain second-order schemes both in time and space. Numerical examples with comparisons among the proposed schemes and the existing ones verify the theoretical analysis and show that the present schemes exhibit better performances than the known ones.