English

Recovery of the rod cross section shape

Numerical Analysis 2025-02-19 v1 Numerical Analysis Mathematical Physics Classical Analysis and ODEs math.MP

Abstract

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.

Keywords

Cite

@article{arxiv.2502.12368,
  title  = {Recovery of the rod cross section shape},
  author = {Vladislav V. Kravchenko and Sergii M. Torba and Alexander O. Vatulyan},
  journal= {arXiv preprint arXiv:2502.12368},
  year   = {2025}
}

Comments

19 pages, 8 figures. To appear in Boletin de la Sociedad Matematica Mexicana