In this article, the Adomian Decomposition Method (ADM) is used to study the harmonic oscillators [6]. The obtained discrete solutions using ADM are compared with the Runge-Kutta (RK) method, Single-term Haar wavelet series (STHW) and ODE45 solutions of the harmonic oscillators and are found to be very accurate. Solution and Error graphs for discrete and exact solutions are presented in a graphical form to show efficiency of this method. This ADM can be easily implemented in a digital computer and the solution can be obtained for any length of time.

In this article, the problem of optimal control of time-varying singular systems with quadratic performance index has been studied via Adomian Decomposition Method (ADM). The results obtained via RK-Butcher algorithm (RKB)[10] and ADM are compared with the exact solutions of the time-varying optimal control of linear singular systems. It is observed that the results obtained using ADM is closer to the true solution of the problem. Error graphs for the simulated results and exact solutions are presented in graphical form to highlight the efficiency of the ADM. This ADM can be easily implemented in a digital computer and the solution can be obtained for any length of time.