A high-order implicit–explicit Runge–Kutta type scheme for the numerical solution of the Kuramoto–Sivashinsky equation
A high-order implicit–explicit Runge–Kutta type scheme for the numerical solution of the Kuramoto–Sivashinsky equation
复制标题
Kuramoto-Sivashinsky 方程数值解的高阶隐式-显式 Runge-Kutta 型格式
DOI：
10.1080/00207160.2020.1814262
复制
发表时间：
2020
影响因子：
1.8
通讯作者：
Chowdhury, A.
中科院分区：
文献类型：
--
作者：
Bhatt, H. P.;Chowdhury, A.
这份手稿是关注的发展和实施的数值计划，研究时空的解决方案配置文件的著名的Kuramoto-Sivashinsky方程与适当的初始和边界条件。提出了一种基于四阶龙格-库塔的时间沿着隐-显格式和空间紧致高阶差分格式。该方案充分利用了直线法和部分分式分解技术，在每个时间步只需求解两个向后的欧拉型线性方程组即可得到解。通过对几个算例的检验以及与相关已知格式的数值结果比较，研究了该格式的性能。数值计算结果表明，该格式比已有的Kuramoto-Sivashinsky方程格式具有更高的精度和可靠性。
This manuscript is concerned with the development and the implementation of a numerical scheme to study the spatio-temporal solution profile of the well-known Kuramoto–Sivashinsky equation with appropriate initial and boundary conditions. A fourth-order Runge–Kutta based implicit–explicit scheme in time along with compact higher-order finite difference scheme in space is introduced. The proposed scheme takes full advantage of the method of line (MOL) and partial fraction decomposition techniques, therefore, it just needs to solve two backward Euler-type linear systems at each time step to get the solution. Performance of the scheme is investigated by testing it on some test examples and by comparing numerical results with relevant known schemes. The numerical results showed that the proposed scheme is more accurate and reliable than existing schemes to solve Kuramoto–Sivashinsky equation.