In this paper, a Green’s function based iterative algorithm is proposed to solve strong nonlinear oscillators. The method’s essential part is based on finding an appropriate Green’s function that will be incorporated into a linear integral operator. An application of fixed point iteration schemes such as Picard’s or Mann’s will generate an iterative formula that gives reliable approximations to the true periodic solutions that characterize these kinds of equations. The applicability and stability of the method will be tested through numerical examples. Since exact solutions to these equations usually do not exist, the proposed method will be tested against other popular numerical methods such as the modified homotopy perturbation, the modified differential transformation, and the fourth-order Runge–Kutta methods.
Green’s Function Iterative Approach for Solving Strongly Nonlinear Oscillators
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received April 10, 2016; final manuscript received May 10, 2017; published online June 16, 2017. Assoc. Editor: Firdaus Udwadia.
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Abukhaled, M. (June 16, 2017). "Green’s Function Iterative Approach for Solving Strongly Nonlinear Oscillators." ASME. J. Comput. Nonlinear Dynam. September 2017; 12(5): 051021. https://doi.org/10.1115/1.4036813
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