In this paper, Homotopy Analysis Method (HAM) is applied to obtain approximate analytical solution of modified Kuramoto–Sivashinsky (KS) equation. HAM provides a simple way to adjust and control the convergence region of the series solution by introducing several parameters, namely, the auxiliary parameter, h, the auxiliary function, H(x; t), the initial guess, u0(x; t) and the auxiliary linear operator, L; as stated in . The obtained results show that HAM yields approximate analytical solutions which are quite close to the exact solution of KS equation, which proves the strength of HAM.
Kurulay, Muhammet; Secer, Aydin; and Akinlar, Ali
"A New Approximate Analytical Solution of Kuramoto – Sivashinsky Equation Using Homotopy Analysis Method,"
Applied Mathematics & Information Sciences: Vol. 07:
1, Article 33.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol07/iss1/33