Reproducing kernel Hilbert space method for the solutions of generalized Kuramoto–Sivashinsky equation

Abstract

Reproducing kernel Hilbert space method is given for the solution of generalized Kuramoto–Sivashinsky equation. Reproducing kernel functions are obtained to get the solution of the generalized Kuramoto–Sivashinsky equation. Two examples have been introduced to prove the accuracy of the method. The obtained results show that the reproducing kernel Hilbert space method gives approximate analytical solutions which are very close to the exact solution of the generalized Kuramoto–Sivashinsky equation, which demonstrates the power of the proposed technique. We prove the efficiency of the reproducing kernel Hilbert space method in this paper.

Keywords

• generalized kuramoto–sivashinsky equation
• reproducing kernel functions
• hilbert spaces