30 citations · 63 across the 11 of their papers we have counts for
12 papers
Polynomial Difference Schemes with Energy and Momentum Multipliers on Orthogonal Uniform Meshes: Stencil Restrictions and Monge--Ampère-Type Examples
E. I. Kaptsov
Experience with invariant finite-difference schemes for one-dimensional hydro\-dynamic-type equations for a function suggests that nonlinear polynomial schemes on orthogon…
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…
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…
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-…
Group classification of the two-dimensional magnetogasdynamics equations in Lagrangian coordinates
S. V. Meleshko, E. I. Kaptsov, S. Moyo +1
The present paper is devoted to the group classification of magnetogasdynamics equations in which dependent variables in Euler coordinates depend on time and two spatial coordinate…
Symmetries and conservation laws of the one-dimensional shallow water magnetohydrodynamics equations in Lagrangian coordinates
S. V. Meleshko, V. A. Dorodnitsyn, E. I. Kaptsov
Symmetries of the one-dimensional shallow water magnetohydrodynamics equations (SMHD) in Gilman's approximation are studied. The SMHD equations are considered in case of a plane an…