The multistep finite difference fractional steps method for a class of viscous wave equations
The multistep finite difference fractional steps method for a class of viscous wave equations
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DOI：
10.1002/mma.1371
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发表时间：
2010-09
影响因子：
2.9
通讯作者：
Zhiyue Zhang
中科院分区：
文献类型：
--
作者：
Zhiyue Zhang
本文提出了一种新的适用于粘性波动方程并行计算的多步分数阶有限差分方法。采用了变分法、差分算子的乘性交换规则、高阶差分算子的分解和先验估计等技术。证明了该格式在时间和空间方向上都是二阶的。利用Von Neumann线性稳定性分析证明了新格式对初值是无条件稳定的。实验表明，该方法对于求解生命科学中的粘性波动方程是非常有效的。版权所有© 2010约翰威利父子有限公司.
In this paper, a new multistep finite difference fractional method applicable to parallel arithmetic for viscous wave equation is proposed. Some techniques, such as calculus of variations, multiplicative commutation rule of difference operators, decomposition of high‐order difference operators and priori estimates are adopted. It is shown that the scheme is second‐order in temporal and spacial direction in the l2 norm. The new scheme is unconditionally stable for initial value by using the Von Neumann linear stability analysis. Experiments show that the new method is very efficient for solving viscous wave equation, which is of vital importance in life sciences. Copyright © 2010 John Wiley & Sons, Ltd.