Optimal Parameters for Nonlinear Hirota-Satsuma Coupled KdV System by Using Hybrid Firefly Algorithm with Modified Adomian Decomposition

Omar Saber Qasim (Department of Mathematics, University of Mosul, Mosul)
Karam Adel Abed (Department of Mathematics, University of Mosul, Mosul)
Ahmed F. Qasim (Department of Mathematics, University of Mosul, Mosul)

Journal of Mathematical and Fundamental Sciences
Vol. 52 No. 3 (2020)

In this paper, several parameters of the non-linear Hirota-Satsuma coupled KdV system were estimated using a hybrid between the Firefly Algorithm (FFA) and the Modified Adomian decomposition method (MADM). It turns out that optimal parameters can significantly improve the solutions when using a suitably selected fitness function for this problem. The results obtained show that the approximate solutions are highly compatible with the exact solutions and that the hybrid method FFA_MADM gives higher efficiency and accuracy compared to the classic MADM method.