An Accurate Method for Solving the Undamped Duffing Equation with Cubic Nonlinearity

Muhammed I. Syam; Muhammad Asif Raja; Mahmmoud M. Syam; H. M. Jaradat

doi:10.1007/s40819-018-0502-1

An Accurate Method for Solving the Undamped Duffing Equation with Cubic Nonlinearity

Muhammed I. Syam, Muhammad Asif Raja, Mahmmoud M. Syam, H. M. Jaradat

Department of Mathematical Sciences

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

1 Citation (Scopus)

Abstract

In this paper, we study the strongly nonlinear undamped duffing equation for undamped oscillators. We present the physical and the mathematical model of nonlinear Duffing equation for undamped oscillators. The reproducing kernal Hilbert space method (RKHSM) is employed to compute an approximation to the solution of this problem. The validity of the RKHSM is ascertained by comparing our results with numerical results and other methods in the literature. The results reveal that the proposed analytical method can achieve excellent results in predicting the solutions of such problems. The existences of the solution is proved. In addition, the uniformly convergent of the proposed method is investigated.

Original language	English
Article number	69
Journal	International Journal of Applied and Computational Mathematics
Volume	4
Issue number	2
DOIs	https://doi.org/10.1007/s40819-018-0502-1
Publication status	Published - Apr 1 2018

Keywords

Duffing equation
Nonlinear boundary value problem
Reproducing kernal Hilbert space method

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1007/s40819-018-0502-1

Cite this

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title = "An Accurate Method for Solving the Undamped Duffing Equation with Cubic Nonlinearity",

abstract = "In this paper, we study the strongly nonlinear undamped duffing equation for undamped oscillators. We present the physical and the mathematical model of nonlinear Duffing equation for undamped oscillators. The reproducing kernal Hilbert space method (RKHSM) is employed to compute an approximation to the solution of this problem. The validity of the RKHSM is ascertained by comparing our results with numerical results and other methods in the literature. The results reveal that the proposed analytical method can achieve excellent results in predicting the solutions of such problems. The existences of the solution is proved. In addition, the uniformly convergent of the proposed method is investigated.",

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author = "Syam, {Muhammed I.} and Raja, {Muhammad Asif} and Syam, {Mahmmoud M.} and Jaradat, {H. M.}",

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AU - Syam, Muhammed I.

AU - Raja, Muhammad Asif

AU - Syam, Mahmmoud M.

AU - Jaradat, H. M.

PY - 2018/4/1

Y1 - 2018/4/1

N2 - In this paper, we study the strongly nonlinear undamped duffing equation for undamped oscillators. We present the physical and the mathematical model of nonlinear Duffing equation for undamped oscillators. The reproducing kernal Hilbert space method (RKHSM) is employed to compute an approximation to the solution of this problem. The validity of the RKHSM is ascertained by comparing our results with numerical results and other methods in the literature. The results reveal that the proposed analytical method can achieve excellent results in predicting the solutions of such problems. The existences of the solution is proved. In addition, the uniformly convergent of the proposed method is investigated.

AB - In this paper, we study the strongly nonlinear undamped duffing equation for undamped oscillators. We present the physical and the mathematical model of nonlinear Duffing equation for undamped oscillators. The reproducing kernal Hilbert space method (RKHSM) is employed to compute an approximation to the solution of this problem. The validity of the RKHSM is ascertained by comparing our results with numerical results and other methods in the literature. The results reveal that the proposed analytical method can achieve excellent results in predicting the solutions of such problems. The existences of the solution is proved. In addition, the uniformly convergent of the proposed method is investigated.

KW - Duffing equation

KW - Nonlinear boundary value problem

KW - Reproducing kernal Hilbert space method

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An Accurate Method for Solving the Undamped Duffing Equation with Cubic Nonlinearity

Abstract

Keywords

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