Solving Kuramoto–Sivashinsky equation by the new iterative method and estimate the optimal parameters by using PSO algorithm

Abstract

In this study, optimal parameters estimation is performed for non-linear (Kuramoto-Sivashinsky) equation using a crossbred method between Particle swarm optimization (PSO) algorithm and (NIM) technique and for the appropriateness we call it (PSO-NIM). It turns out that the optimal parameters significantly improve the solutions when we use a fitness function suitable for the issue. The results confirmed that the get approximate solutions are in suitable pact with the exact solutions and the proposed method provides high accuracy and efficiency in comparison with (NIM) which use traditionally chosen parameters.