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Bibliographic Details
Main Authors: Kaptsov, E. I., Dorodnitsyn, V. A.
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2503.03369
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Table of Contents:
  • It is demonstrated that one of the equations from the Lie classification list of second-order ODEs is a first integral of the Schwarz equation. As symmetry-preserving finite-difference schemes have been previously constructed for both equations, the preservation of a similar connection between these schemes is studied. It is shown that the schemes for the Schwarz equation and the second-order ODE (with an arbitrary constant $C$) can be related through a Bäcklund-type difference transformation. In addition, previously unexamined aspects of the difference scheme for the second-order ODE are discussed, including its singular solution and the complete set of difference first integrals for the case $C^2=4$.