66 citations · 304 across the 25 of their papers we have counts for
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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 with conservation laws preservation for one-dimensional MHD equations
E. I. Kaptsov, V. A. Dorodnitsyn
Invariant finite-difference schemes are considered for one-dimensional magnetohydrodynamics (MHD) equations in mass Lagrangian coordinates for the cases of finite and infinite cond…
Conservative invariant finite-difference schemes for the modified shallow water equations in Lagrangian coordinates
V. A. Dorodnitsyn, E. I. Kaptsov, S. V. Meleshko
The one-dimensional modified shallow water equations in Lagrangian coordinates are considered. It is shown the relationship between symmetries and conservation laws in Lagrangian c…
Invariant conservative difference schemes for shallow water equations in Eulerian and Lagrangian coordinates
V. A. Dorodnitsyn, E. I. Kaptsov
The one-dimensional shallow water equations in Eulerian coordinates are considered. Relations between symmetries and conservation laws for the potential form of the equations, and…
Symmetry-preserving discrete schemes for some heat transfer equations
Margarita Bakirova, Vladimir Dorodnitsyn, Roman Kozlov
Lie group analysis of differential equations is a generally recognized method, which provides invariant solutions, integrability, conservation laws etc. In this paper we present th…