Numeric-Analytic Solutions for Nonlinear Oscillators via the Modified Multi-Stage Decomposition Method

Abstract

This work deals with a new modified version of the Adomian-Rach decomposition method (MDM). The MDM is based on combining a series solution and decomposition method for solving nonlinear differential equations with Adomian polynomials for nonlinearities. With application to a class of nonlinear oscillators known as the Lienard-type equations, convergence and error analysis are discussed. Several physical problems modeled by Lienard-type equations are considered to illustrate the effectiveness, performance and reliability of the method. In comparison to the 4th Runge-Kutta method (RK4), highly accurate solutions on a large domain are obtained.

Keywords

• nonlinear oscillators
• Lienard equation
• van der Pol equation
• Power series method
• Adomian polynomials
• Convergence
• Error analysis