Colloquium
3:00 p.m.
Math Annex 1100
Vladimir Dorodnitsyn
Keldysh Institute of Applied Mathematics
Russian Academy of Sciences
Moscow
Application of Lie Groups to Difference Equations:
how to construct the invariant difference model
Symmetries are fundamental features of the differential equations
of mathematical physics. They yield a number of useful properties
such as symmetry reduction of PDEs, existence of various types of
invariant solutions, integrability of ODEs, conservation laws for
invariant variational problems, etc. Therefore, for preserving
symmetries in discrete schemes, we retain qualitative properties
of the underlying differential equations. We exhibit procedures
that have been developed to preserve Lie group properties while
constructing finite difference schemes and meshes. Examples for
ODEs and PDEs will be considered.
