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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 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…