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nlin.SI2025
Symmetry Approach to Integration of Ordinary Differential Equations with Retarded Argument
Vladimir Dorodnitsyn, Roman Kozlov, Sergey Meleshko
We review studies on the application of Lie group methods to delay ordinary differential equations (DODEs). For first- and second-order DODEs with a single delay parameter that dep…
math.NA2025
Symmetry-Preserving Finite-Difference Schemes and Auto-Bäcklund Transformations for the Schwarz Equation
E. I. Kaptsov, V. A. Dorodnitsyn
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-differ…