A high‐order ADI finite difference scheme for a 3D reaction‐diffusion equation with neumann boundary condition
A high‐order ADI finite difference scheme for a 3D reaction‐diffusion equation with neumann boundary condition
复制标题
DOI：
10.1002/num.21726
复制
发表时间：
2013-05
影响因子：
3.9
通讯作者：
Wenyuan Liao
中科院分区：
文献类型：
--
作者：
Wenyuan Liao
本文推广了Liao等人的四阶紧致边界格式。（Numer Methods Partial Differential Equations 18（2002），340-354）的方法应用于3D问题，然后将其与Gu等人的四阶紧致交替方向隐式（ADI）方法联合收割机组合。（J Comput Appl Math 155（2003），1-17）来求解具有Neumann边界条件的3D反应-扩散方程。首先，用基于Padé近似的紧致四阶差分方法求解反应扩散方程，然后将其与ADI方法和四阶紧致格式相结合，逼近Neumann边界条件，以获得空间上的四阶精度。虽然数值方法的无条件稳定性得到了证明，但通过应用Richardson外推技术，在时间维上的精度提高到了四阶，并给出了几个数值例子来证明所提出的新算法的精度和效率。© 2012 Wiley Periodicals，Inc. Numer Methods Partial Differential Eq，2013
In this article, we extend the fourth‐order compact boundary scheme in Liao et al. (Numer Methods Partial Differential Equations 18 (2002), 340–354) to a 3D problem and then combine it with the fourth‐order compact alternating direction implicit (ADI) method in Gu et al. (J Comput Appl Math 155 (2003), 1–17) to solve the 3D reaction‐diffusion equation with Neumann boundary condition. First, the reaction‐diffusion equation is solved with a compact fourth‐order finite difference method based on the Padé approximation, which is then combined with the ADI method and a fourth‐order compact scheme to approximate the Neumann boundary condition, to obtain fourth order accuracy in space. The accuracy in the temporal dimension is improved to fourth order by applying the Richardson extrapolation technique, although the unconditional stability of the numerical method is proved, and several numerical examples are presented to demonstrate the accuracy and efficiency of the proposed new algorithm. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013