### September 13, Daniel Robertz, University of Plymouth

*Algorithmic Approach to Strong Consistency Analysis of
Finite Difference Approximations to PDE Systems
*

The most common numerical method for solving partial
differential equations is the finite difference method.
Consistency of a finite difference scheme with a given
PDE is a basic requirement for this method.
Earlier work by V. P. Gerdt and the speaker introduced
the notion of strong consistency that takes into account
the differential ideal and the difference ideal associated
with the PDE system and the approximating difference system,
respectively.
We present an algorithmic approach to strong consistency for
polynomially nonlinear PDE systems based on a new decomposition
technique for nonlinear partial difference systems that is
analogous to the differential Thomas decomposition. This is
joint work with Vladimir P. Gerdt (JINR, Dubna).

Video
### October 18, Omar Leon Sanchez, University of Manchester

*Differentially large fields*

Recall that a field K is large if it is existentially closed in the field of Laurent series K((t)). Examples of such fields are the complex, the real, and the p-adic numbers. This class of fields has been exploited significantly by F. Pop and others in inverse Galois-theoretic problems. In recent work with Tressl we introduced and explored a differential analogue of largeness, that we conveniently call “differentially large”. I will present some properties of such fields and characterise them using formal Laurent series and to even construct “natural” examples (which ultimately yield examples of DCFs and CODFs... acronyms that will be explained in the talk). Time permitting I will mention some applications to Parameterized PV theory.