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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-…