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

The present article is designed to supply two different numerical solutions for solving Kuramoto-Sivashinsky equation. We have made an attempt to develop a numerical solution via the use of Sinc-Galerkin method for Kuramoto-Sivashinsky equation, Sinc approximations to both derivatives and indefinite integrals reduce the solution to an explicit system of algebraic equations. The fixed point theory is used to prove the convergence of the proposed methods. For comparison purposes, a combination of a Crank-Nicolson formula in the time direction, with the Sinc-collocation in the space direction is presented, where the derivatives in the space variable are replaced by the necessary matrices to produce a system of algebraic equations. In addition, we present numerical examples and comparisons to support the validity of these proposed methods.