Multistage Bernstein collocation method for solving strongly nonlinear damped systems

Ahmad Sami Bataineh, Abd Alkreem Al-Omari, Osman Rasit Isik, Ishak Hashim

Research output: Contribution to journalArticle

Abstract

In this paper, we propose an approximate solution method, called multistage Bernstein collocation method (MBCM), to solve strongly nonlinear damped systems. The method is given with an error analysis. The systems investigated include step function external excitation and periodical function external excitation. We found that the MBCM gives more accurate approximate solutions than the standard collocation method. Since MBCM splits the domain of the problem (Formula presented.) into n parts, one can overcome oscillations arising from the standard collocation method by increasing n. The results obtained from MBCM compare favorably with that of the fourth-order Runge–Kutta method (RK4).

Original languageEnglish
JournalJVC/Journal of Vibration and Control
DOIs
Publication statusAccepted/In press - 1 Jan 2018

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Nonlinear systems
Error analysis

Keywords

  • Bernstein polynomials
  • error analysis
  • multistage Bernstein polynomials
  • nonlinear damped system
  • operational matrix of differentiation

ASJC Scopus subject areas

  • Materials Science(all)
  • Automotive Engineering
  • Aerospace Engineering
  • Mechanics of Materials
  • Mechanical Engineering

Cite this

Multistage Bernstein collocation method for solving strongly nonlinear damped systems. / Bataineh, Ahmad Sami; Al-Omari, Abd Alkreem; Rasit Isik, Osman; Hashim, Ishak.

In: JVC/Journal of Vibration and Control, 01.01.2018.

Research output: Contribution to journalArticle

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