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<p>The eigenvalues and eigenfunctions of the Sturm–Liouville problem are found with the help of three-point difference schemes with high order of accuracy constructed on an arbitrary nonuniform grid. The Newton iterative method was developed for solving three-point difference schemes of this kind. Numerical experiments were performed, in particular, in order to compare the results obtained by using a difference scheme of the sixth order of accuracy with the results of a classical difference scheme of the second order of accuracy. The accumulated results confirm the efficiency of the proposed approach.</p>

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Algorithm for Solving the Sturm–Liouville Problem Based on Three-Point Difference Schemes with High Order of Accuracy

  • 期刊论文

  • 发表日期：

    2026年5月19日

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  • A. V. Kunynets,
  • M. V. Kutniv,
  • N. V. Khomenko

摘要

The eigenvalues and eigenfunctions of the Sturm–Liouville problem are found with the help of three-point difference schemes with high order of accuracy constructed on an arbitrary nonuniform grid. The Newton iterative method was developed for solving three-point difference schemes of this kind. Numerical experiments were performed, in particular, in order to compare the results obtained by using a difference scheme of the sixth order of accuracy with the results of a classical difference scheme of the second order of accuracy. The accumulated results confirm the efficiency of the proposed approach.