For systems of partial differential equations in three spatial dimensions, dynamical
conservation laws holding on volumes, surfaces, and curves, as well as topological …

New technologies play a central role in damage prevention of artistic and cultural heritage.
The literature is ourishing of mathematical models that describe the process of corrosion due …

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 …

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 …

We show a novel systematic way to construct conservative finite difference schemes for
quasilinear first-order systems of ordinary differential equations with conserved quantities. In …

This paper introduces sufficient conditions to determine conservation laws of diffusion
equations of arbitrary fractional order in time. Numerical methods that satisfy discrete …

Conservation laws are among the most fundamental geometric properties of a partial
differential equation (PDE), but few known finite difference methods preserve more than one …

The explicit formulation of the general inverse problem on conservation laws is presented for
the first time. Within this problem, one aims to derive the general form of systems of …

A procedure for obtaining the Lie point symmetries of a difference scheme for a nonlinear
sine-Gordan equation is presented. The invariant discretization of the first order of accuracy …

We show the arbitrarily long-term stability of conservative methods for autonomous ODEs.
Given a system of autonomous ODEs with conserved quantities, if the preimage of the …