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math.NA2020★ 17 cited
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…
math-ph2020★ 2 cited
Invariant Conservation Law-Preserving Discretizations of Linear and Nonlinear Wave Equations
A. F. Cheviakov, V. A. Dorodnitsyn, E. I. Kaptsov
Symmetry- and conservation law-preserving finite difference discretizations are obtained for linear and nonlinear one-dimensional wave equations on five- and nine-point stencils, u…