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This manuscript introduces a fourth-order Runge-Kutta based implicit-explicitscheme in time along with compact fourth-order finite difference scheme inspace for the solution of one-dimensional Kuramoto-Sivashinsky equation withperiodic and Dirichlet boundary conditions, respectively. The proposed schemetakes full advantage of method of line (MOL) and partial fraction decompositiontechniques, therefore it just need to solve two backward Euler-type linearsystems at each time step to get the solution. Performance of the scheme isinvestigated by testing it on some test examples and by comparing numericalresults with relevant known schemes. It is found that the proposed scheme ismore accurate and reliable than existing schemes to solve Kuramoto-Sivashinskyequation.

A compact fourth-order implicit-explicit Runge-Kutta type scheme for numerical solution of the Kuramoto-Sivashinsky equation