66 citations · 304 across the 25 of their papers we have counts for
25 papers
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…
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…
Delay ordinary differential equations: from Lagrangian approach to Hamiltonian approach
Vladimir Dorodnitsyn, Roman Kozlov, Sergey Meleshko
The paper suggests a Hamiltonian formulation for delay ordinary differential equations (DODEs). Such equations are related to DODEs with a Lagrangian formulation via a delay analog…
Invariant conservative finite-difference schemes for the one-dimensional shallow water magnetohydrodynamics equations in Lagrangian coordinates
E. I. Kaptsov, V. A. Dorodnitsyn
Invariant finite-difference schemes for the one-dimensional shallow water equations in the presence of a magnetic field for various bottom topographies are constructed. Based on th…
Lagrangian formalism and Noether-type theorems for second-order delay ODEs
Vladimir A. Dorodnitsyn, Roman V. Kozlov, Sergey V. Meleshko
The Lagrangian formalism for variational problem for second-order delay ordinary differential equations (DODEs) is developed. The Noether-type operator identities and theorems for…
Invariant Finite-Difference Schemes for Cylindrical One-Dimensional MHD Flows with Conservation Laws Preservation
E. I. Kaptsov, V. A. Dorodnitsyn, S. V. Meleshko
On the basis of the recent group classification of the one-dimensional magnetohydrodynamics (MHD) equations in cylindrical geometry, the construction of symmetry-preserving finite-…