Numerical solutions of the generalized Kuramoto–Sivashinsky equation using B-spline functions

A numerical technique based on the finite difference and collocation methods is presented for the solution of generalized Kuramoto–Sivashinsky (GKS) equation. The derivative matrices between any two families of B-spline functions are presented and are utilized to reduce the solution of GKS equation to the solution of linear algebraic equations. Numerical simulations for five test examples have been demonstrated to validate the technique proposed in the current paper. It is found that the simulating results are in good agreement with the exact solutions.