Abstract
A numerical method for finding the solution of Duffing-harmonic oscillator is proposed. The approach is based on hybrid functions approximation. The properties of hybrid functions that consist of block-pulse and Chebyshev cardinal functions are discussed. The associated operational matrices of integration and product are then utilized to reduce the solution of a strongly nonlinear oscillator to the solution of a system of algebraic equations. The method is easy to implement and computationally very attractive. The results are compared with the exact solution and results from several recently published methods, and the comparisons showed proper accuracy of this method.
Highlights
Most phenomena in our world are essentially nonlinear and are described by nonlinear ordinary differential equations
Razzaghi and Marzban [23] applied the hybrid of block-pulse and Chebyshev functions to find approximate solution of systems with delays in state and control
We present the properties of hybrid functions which consist of block-pulse functions plus Chebyshev cardinal functions similar to [27, 29, 30]
Summary
Most phenomena in our world are essentially nonlinear and are described by nonlinear ordinary differential equations. Razzaghi and Marzban [23] applied the hybrid of block-pulse and Chebyshev functions to find approximate solution of systems with delays in state and control. Solution of time-varying delay systems is approximated using hybrid of block-pulse functions and Legendre polynomials in [24]. Journal of Difference Equations in [26], a direct method for solving multidelay systems using hybrid of block-pulse functions and Taylor series is presented. We introduce an alternative numerical method to solve Duffing-harmonic oscillator. The operational matrices of integration and product are given These matrices are used to evaluate the coefficients of the hybrid function for the solution of strongly nonlinear oscillators.
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