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<p>A direct method for solving the inverse problem of determining the shape of the cross-section of a rod is proposed. The method is based on Neumann series of Bessel functions representations for solutions of Sturm-Liouville equations. The first coefficient of the representation is sufficient for the recovery of the unknown function. A system of linear algebraic equations for finding this coefficient is obtained. The proposed method leads to an efficient numerical algorithm.</p>

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Recovery of the rod cross-section shape

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年3月6日

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  • Vladislav V. Kravchenko,
  • Sergii M. Torba,
  • Alexander O. Vatulyan

摘要

A direct method for solving the inverse problem of determining the shape of the cross-section of a rod is proposed. The method is based on Neumann series of Bessel functions representations for solutions of Sturm-Liouville equations. The first coefficient of the representation is sufficient for the recovery of the unknown function. A system of linear algebraic equations for finding this coefficient is obtained. The proposed method leads to an efficient numerical algorithm.