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

• Published in: Journal of Taibah University for Science Vol. 13; no. 1; pp. 661 - 669
• Main Authors: Akgül, Ali, Bonyah, Ebenezer
• Format: Journal Article
• Language: English
• Published: Taylor & Francis 11.12.2019; Taylor & Francis Group
• Subjects: accuracy; equations; Generalized Kuramoto-Sivashinsky equation; Hilbert spaces; reproducing kernel functions; seeds; solutions
• ISSN: 1658-3655; 1658-3655
• DOI: 10.1080/16583655.2019.1618547

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.