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Reproducing Kernel Method for Solving Nonlinear Oscillators Under Damping Effect

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Abstract

The current paper is devoted to introducing a semi-analytical technique for the numerical solution of nonlinear oscillators under the damping effect by using the reproducing kernel Hilbert space method. The proposed scheme is a hybrid of the reproducing kernel Hilbert space and the perturbation methods. This method finds solutions to periodic and nonlinear problems by converting to a system of linear differential equations. Finally, some test problems are given to illustrate the validity of the novel algorithm. Also, the presented numerical results using the method are compared with the numerical solutions of the fourth-order Runge–Kutta method. The numerical results reported show that the present method can provide very accurate approximate solutions.

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Acknowledgements

This article has been supported by Kharazmi University and Iran National Science Foundation (INSF). The authors thank both institutions for their good support during this study.

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Authors and Affiliations

  1. Iran National Science Foundation: INSF, No. 33, Fifth Avenue, North Kargar Street, Tehran, Iran

    Farhad Moradi

  2. Mosaheb Institute of Mathematics, Kharazmi University, No. 50, Taleghani Avenue, Tehran, 1561836314, Iran

    Farhad Moradi

  3. Faculty of Mathematical Sciences and Computer, Kharazmi University, No. 50, Taleghani Avenue, Tehran, 1561836314, Iran

    Shahnam Javadi

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  1. Farhad Moradi
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  2. Shahnam Javadi
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Correspondence to Farhad Moradi.

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Moradi, F., Javadi, S. Reproducing Kernel Method for Solving Nonlinear Oscillators Under Damping Effect. Iran J Sci Technol Trans Sci 44, 763–772 (2020). https://doi.org/10.1007/s40995-020-00868-6

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  • DOI: https://doi.org/10.1007/s40995-020-00868-6

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