Convergence analysis and error estimate of second-order implicit-explicit scheme for Gray-Scott model
Convergence analysis and error estimate of second-order implicit-explicit scheme for Gray-Scott model
复制标题
Gray-Scott模型二阶隐式-显式格式的收敛性分析与误差估计
DOI：
10.1080/00207160.2021.1896711
复制
发表时间：
--
影响因子：
1.8
通讯作者：
Jinrong Wang
中科院分区：
文献类型：
--
作者：
Fangying Song;Jun Zhang;Jinrong Wang
在本文中，我们提出了一个二阶隐式显式（IMEX）的时间推进格式的格雷斯科特（GS）模型。为了在时间上获得快速、稳定和有效的格式，我们提出了一种求解GS模型的线性二阶时间推进格式。我们证明了该方案的线性稳定性和收敛性。我们的数值格式的优点是稳定的，即不需要对非线性项进行其他的稳定性限制，只需要一个相对较小的时间步长。此外，我们证明了数值解达到二阶精度的时间。最后通过数值实验验证了该格式在时间和空间上的精度。数值算例表明，IMEX格式对GS模型的计算精度和效率是有效的。
In this paper, we propose a second-order implicit–explicit (IMEX) time-stepping scheme for the Gray-Scott (GS) model. In order to achieve a fast, stable and efficient scheme in time, we develop a linear second-order time-stepping scheme for solving GS model. We prove the linear stability and convergence of the proposed scheme. The advantage of our numerical scheme is stable, that is, there is no need for other stability restrictions to the nonlinear terms, only a relatively small time step is needed. Moreover, we prove that the numerical solutions achieve second-order accuracy in the time. Finally, several numerical experiments are conducted to verify the accuracy both in space and time of the numerical scheme. Numerical examples illustrate the accuracy and efficiency of the IMEX scheme is effective for the GS model.