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<p>A constructive approach is proposed for the approximate finding of periodic solutions of differential systems with deviating argument and non-linearities satisfying the Lipschitz condition in a bounded region. Under suitable assumptions, the method allows one to prove solvability based on computational results. We describe a computationally less demanding version of the scheme involving trigonometric polynomial interpolation, in which higher-order approximations are constructed without symbolic integration. The practical use of the method is demonstrated with numerical examples.</p>

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Parameterization and Trigonometric Approximation of Periodic Solutions of Non-linear Equations with Deviating Arguments

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月25日

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  • András Rontó

摘要

A constructive approach is proposed for the approximate finding of periodic solutions of differential systems with deviating argument and non-linearities satisfying the Lipschitz condition in a bounded region. Under suitable assumptions, the method allows one to prove solvability based on computational results. We describe a computationally less demanding version of the scheme involving trigonometric polynomial interpolation, in which higher-order approximations are constructed without symbolic integration. The practical use of the method is demonstrated with numerical examples.