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A high-order implicit–explicit Runge–Kutta type scheme for the numerical solution of the Kuramoto–Sivashinsky equation
International Journal of Computer Mathematics ( IF 1.8 ) Pub Date : 2020-09-11 , DOI: 10.1080/00207160.2020.1814262
H. P. Bhatt 1 , A. Chowdhury 2
Affiliation  

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.



中文翻译:

Kuramoto-Sivashinsky方程数值解的高阶隐式-显性Runge-Kutta类型方案

该手稿涉及数值方案的开发和实施,以研究具有适当初始和边界条件的著名Kuramoto-Sivashinsky方程的时空解轮廓。介绍了基于时间的基于Runge-Kutta的四阶隐式-显式方案以及紧凑的空间高阶有限差分方案。该方案充分利用了线法和部分分数分解技术的优势,因此,只需在每个时间步求解两个后向欧拉型线性系统即可得到解。通过在一些测试示例上对其进行测试并将数值结果与相关的已知方案进行比较,可以研究该方案的性能。

更新日期:2020-09-11
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