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Periodic solutions for certain non-smooth oscillators by iterated homotopy perturbation method combined with modified Lindstedt-Poincaré technique

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Abstract

In this paper, a new technique is introduced by combining Homotopy perturbation method and modified Lindstedt-Poincaré technique to obtain the periodic solutions of certain non-smooth oscillators. In this technique, homotopy perturbation method is re-written in iterative form to linearize perturbation process by homotopy, and then, the modified Lindstedt-Poincaré method is utilized to obtain next approximation for each iteration step. We realize that this new technique works very well for the whole range of initial amplitudes, and the excellent agreement of the approximate frequencies and periodic solutions with the exact ones has been confirmed and discussed. Only one or two iterations lead to high accuracy of the solutions. The result obtained and comparison with analytical solution and different methods provide confirmation for the validity of the technique.

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  1. Department of Mathematics, Faculty of Science, Ege University, 35100, Bornova, İzmir, Turkey

    Turgut Öziş & Ceren Akçı

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  1. Turgut Öziş
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  2. Ceren Akçı
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Correspondence to Turgut Öziş.

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Öziş, T., Akçı, C. Periodic solutions for certain non-smooth oscillators by iterated homotopy perturbation method combined with modified Lindstedt-Poincaré technique. Meccanica 46, 341–347 (2011). https://doi.org/10.1007/s11012-010-9312-1

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