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

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

doi:10.3390/MATH7060550

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

Mathematics & Statistics

Research output: Contribution to journal › Article › peer-review

17 Citations (Scopus)

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.

Original language	English
Article number	550
Journal	Mathematics
Volume	7
Issue number	6
DOIs	https://doi.org/10.3390/MATH7060550
Publication status	Published - 2019

Keywords

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

ASJC Scopus subject areas

Computer Science (miscellaneous)
Mathematics(all)
Engineering (miscellaneous)

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10.3390/MATH7060550

Cite this

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title = "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 = "Adomian polynomials, Convergence, Error analysis, Lienard equation, Nonlinear oscillators, Power series method, Van der Pol equation",

author = "Az-Zo'bi, {Emad A.} and Kamel Al-Khaled and Amer Darweesh",

note = "Funding Information: This research received no external funding. The authors would like to thank the referees for their valuable comments which helped to improve the manuscript. Also they would like to thank both Mutah University and Jordan University of Science and Technology for motivating and supporting them to be good researchers Publisher Copyright: {\textcopyright} 2019 by the authors.",

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doi = "10.3390/MATH7060550",

language = "English",

volume = "7",

journal = "Mathematics",

issn = "2227-7390",

publisher = "MDPI AG",

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TY - JOUR

T1 - Numeric-analytic solutions for nonlinear oscillators via the modified multi-stage decomposition method

AU - Az-Zo'bi, Emad A.

AU - Al-Khaled, Kamel

AU - Darweesh, Amer

N1 - Funding Information: This research received no external funding. The authors would like to thank the referees for their valuable comments which helped to improve the manuscript. Also they would like to thank both Mutah University and Jordan University of Science and Technology for motivating and supporting them to be good researchers Publisher Copyright: © 2019 by the authors.

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

KW - Adomian polynomials

KW - Convergence

KW - Error analysis

KW - Lienard equation

KW - Nonlinear oscillators

KW - Power series method

KW - Van der Pol equation

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DO - 10.3390/MATH7060550

M3 - Article

AN - SCOPUS:85069924761

SN - 2227-7390

VL - 7

JO - Mathematics

JF - Mathematics

IS - 6

M1 - 550

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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