Enhancing Banach’s contraction method using the particle swarm optimization to solve the system Drinfeld-Sokolov-Wilson

Abstract

Abstract In this manuscript, the system (Drinfeld-Sokolov-Wilson) has been solved using the analytical method (Banach contraction) and then using the intelligent method (particle swarm optimization) to improve the results we obtained from the analytical method, the results we obtained from the hybrid method (BCM - PSO) proved the efficiency of this method by finding (MAE and MSE) compared with the exact solution, and also the results of the analytical and hybrid methods were drawn compared with the exact solution.