Conservation laws: from differential to difference

Prof Peter Hydon (University of Surrey)

Friday 10th October, 2014 16:00-17:00 Maths 204


Famously, Noether's (First) Theorem uses symmetries of a variational problem to generate conservation laws of the corresponding Euler-Lagrange equations. It is less well-known that one can construct conservation laws directly, for a given system of PDEs in Kovalevskaya form, whether or not the system arises from a variational problem. In this talk, I describe how both of these approaches can be used (with appropriate modifications) to find conservation laws of partial difference equations. I also discuss a difference analogue of Noether’s Second Theorem, together with a new intermediate result that links Noether’s First and Second Theorems. These results open up some new ways to obtain finite difference approximations that preserve particular conservation laws and generalized Bianchi identities.


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