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

Emad A. Az-Zo’bi, Kamel Al-Khaled and Amer Darweesh
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Emad A. Az-Zo’bi: Department of Mathematics and Statistics, Mutah University, Mutah, P.O. Box 7, Al-Karak 61710, Jordan
Kamel Al-Khaled: Department of Mathematics, Jordan University of Science and Technology, Irbid 22110, Jordan
Amer Darweesh: Department of Mathematics, Jordan University of Science and Technology, Irbid 22110, Jordan

Mathematics, 2019, vol. 7, issue 6, 1-13

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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