Using differentiation matrices for pseudospectral method solve Duffing Oscillator

We propose a new method, namely, the modified harmonic balance method. This paper also analyses and offers the high-order approximate periodic solutions to the strongly nonlinear oscillator with cubic and harmonic restoring force. The existing harmonic balance method cannot be applied directly to such kind of nonlinear oscillators in the presence of forcing term. It is possible if we rewrite the original form of the nonlinear oscillators. If we do so, the results are valid only for small values of amplitude of the oscillation. Moreover, after applying the existing harmonic balance method, a set of complicated higher-order nonlinear algebraic equations are obtained. Analytical investigation

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A new algorithm used the Chebyshev pseudospectral method to solve the nonlinear second-order Lienard differential equations

Nhat

Lovetskiy

Kulyabov

2019

J. Phys.: Conf. Ser.

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This article presents a numerical method to determine the approximate solutions of the Lienard equations. It is assumed that the second-order nonlinear Linard differential equations on the range [-1, 1] with the given boundary values. We have to build a new algorithm to find approximate solutions to this problem. This algorithm based on the pseudospectral method using the Chebyshev differentiation matrix (CPM). In this paper, we used the Mathematica version 10.4 to represent the algorithm, numerical results and graphics. In the numerical results, we made a comparison between the CPMs numerical results and the Mathematica’s numerical results. The biggest odds were very small. Therefore, they will be able to be applied to other nonlinear systems such as the Rayleigh equations and Emden-fowler equations.

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Using differentiation matrices for pseudospectral method solve Duffing Oscillator

Cited by 4 publications

References 13 publications

Reproducing Kernel Method for Solving Nonlinear Oscillators Under Damping Effect

Reproducing Kernel Method for Solving Nonlinear Oscillators Under Damping Effect

A modified harmonic balance method to obtain higher-order approximations to strongly nonlinear oscillators

A new algorithm used the Chebyshev pseudospectral method to solve the nonlinear second-order Lienard differential equations

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