Computational Sinc-scheme for extracting analytical solution for the model Kuramoto-Sivashinsky equation

Abstract

The present article is designed to supply two different numericalsolutions for solving  Kuramoto-Sivashinsky equation. We have madean attempt to develop a numerical solution via the use ofSinc-Galerkin method for  Kuramoto-Sivashinsky equation, Sincapproximations to both derivatives and indefinite integrals reducethe solution to an explicit system of algebraic equations. The fixedpoint theory is used to prove the convergence of the proposedmethods. For comparison purposes, a combination of a Crank-Nicolsonformula in the time direction, with the Sinc-collocation in thespace direction is presented, where the derivatives in the spacevariable are replaced by the necessary matrices to produce a systemof algebraic equations. In addition, we present numerical examplesand comparisons to support the validity of these proposedmethods.