A high-order implicit–explicit Runge–Kutta type scheme for the numerical solution of the Kuramoto–Sivashinsky equation. Issue 6 (3rd June 2021)

• Record Type: Journal Article
• Authors: Bhatt, H. P.; Chowdhury, A.
• Is Part Of: International journal of computer mathematics. Volume 98:Issue 6(2021)
• Page Start: 1254
• Page End: 1273
• Publication Date: 2021-06-03
• Subjects: Implicit–explicit scheme -- Kuramoto–Sivashinsky equation -- partial fraction splitting technique -- compact finite difference -- exponential time differencing; 65; Computers -- Periodicals; Numerical analysis -- Periodicals; Automation -- Periodicals; 004.0151
• DOI: 10.1080/00207160.2020.1814262
• Languages: English
• ISSNs: 0020-7160

Abstract

Abstract : 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.