Numeric-analytic solutions for nonlinear oscillators via the modified multi-stage decomposition method

Emad A. Az-Zo'bi*, Kamel Al-Khaled, Amer Darweesh

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


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.

Original languageEnglish
Article number550
Issue number6
Publication statusPublished - 2019
Externally publishedYes


  • Adomian polynomials
  • Convergence
  • Error analysis
  • Lienard equation
  • Nonlinear oscillators
  • Power series method
  • Van der Pol equation

ASJC Scopus subject areas

  • Mathematics(all)

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