A New Approximate Analytical Solution of Kuramoto - Sivashinsky Equation Using Homotopy Analysis Method - Kurulay, Muhammet; Secer, Aydin; Akinlar, Mehmet Ali (NATURAL SCIENCES PUBLISHING CORP-NSP, 2013)
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, u(0) (x, t) and the auxiliary linear operator, L, as stated in [1]. 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.
Keywords: Kuramoto-Sivashinsky equation; homotopy analysis method; approximate analytical solutions; Maple; Mathematics; Physics