Application of the hybrid Laplace Adomian decomposition method to the nonlinear oscillatory systems

摘要

In this study, a new algorithm is proposed to solve the nonlinear oscillatory systems. The Laplace Adomian decomposition method (LADM) combines the numerical Laplace transform algorithm and the Adomian decomposition method (ADM). The truncated series solutions solved by ADM and LADM both diverge rapidly as the applicable domain increases and do not exhibit periodicity. However, the Pade approximant extends the domain of the truncated series solution to obtain better accuracy and convergence, and the LADM - Pade approximant technique is introduced in this paper order to overcome the drawbacks of the ADM and LADM solutions. Four examples here in are given to show the accuracy in comparison with the fourth-order Runge-Kutta (RK4) solutions, the modified ADM solutions, and the modified differential transform solutions.