The design and analysis of numerical methods are usually guided by the following:(a) von
Neumann analysis using Fourier series expansion of unknowns,(b) the modified differential …

We propose the use of physics-informed neural networks for solving the shallow-water
equations on the sphere in the meteorological context. Physics-informed neural networks …

Under investigation in this work is a generalized higher-order beam equation, which is an
important physical model and describes the vibrations of a rod. By considering Lie symmetry …

This book on integrable systems and symmetries presents new results on applications of
symmetries and integrability techniques to the case of equations defined on the lattice. This …

The one-dimensional shallow water equations in Eulerian coordinates are considered.
Relations between symmetries and conservation laws for the potential form of the equations …

Methods for the design of physical parameterization schemes that possess certain
invariance properties are discussed. These methods are based on different techniques of …

Symmetry-and conservation law-preserving finite difference discretizations are obtained for
linear and nonlinear one-dimensional wave equations on five-and nine-point stencils using …

The one-dimensional shallow water equations in Eulerian and Lagrangian coordinates are
considered. It is shown the relationship between symmetries and conservation laws in …

We carry out the group classification of the class of two-dimensional shallow water
equations with variable bottom topography using an optimized version of the method of …

Two–dimensional optimal classification is performed for two–dimensional shallow water
equations with flat bottom in Cartesian coordinates. In the proof of optimality of subalgebras …