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A fast temporal second-order compact ADI difference scheme for the 2D multi-term fractional wave equation
Numerical Algorithms ( IF 2.1 ) Pub Date : 2020-03-12 , DOI: 10.1007/s11075-020-00910-z
Hong Sun , Zhi-zhong Sun

In this paper, a fast temporal second-order compact ADI scheme is proposed for the 2D time multi-term fractional wave equation. At the super-convergence point, the multi-term Caputo derivative is approximated by combining the order reduction technique with the sum-of-exponential approximation to the kernel function appeared in Caputo derivative. The difference scheme can be solved by the recursion, which reduces the storage and computational cost significantly. The obtained scheme is uniquely solvable. The unconditional convergence and stability of the scheme in the discrete H1-norm are proved by the discrete energy method and the convergence accuracy is second-order in time and fourth-order in space. Numerical example illustrates the efficiency of the scheme.



中文翻译:

二维多项分数波方程的快速时态二阶紧凑ADI差分格式

本文针对二维时间多项式分数波方程,提出了一种快速的时间二阶紧凑型ADI方案。在超收敛点,通过将阶数约简技术与对Caputo导数中的核函数的指数和求和相结合,可以近似多项式Caputo导数。递归可以解决差异方案,从而大大减少了存储和计算成本。所获得的方案是唯一可解的。通过离散能量方法证明了该方案在离散H 1-范数中的无条件收敛性和稳定性,其收敛精度在时间上是二阶的,在空间上是四阶的。数值算例说明了该方案的有效性。

更新日期:2020-03-12
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