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Iterative reproducing kernel method for nonlinear oscillator with discontinuity. (English) Zbl 1202.34074

Summary: The iterative reproducing kernel method is applied to obtain the analytical approximate solution of a nonlinear oscillator with discontinuities. The solution obtained by using the method takes the form of a convergent series with easily computable components. An illustrative example is given to demonstrate the effectiveness of the present method. The results obtained using the scheme presented here show that the numerical scheme is very effective and convenient for the nonlinear oscillator with discontinuities.

MSC:

34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
34A36 Discontinuous ordinary differential equations
34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.
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