This is the first year of a two-year project on the study of geometric theories of higher-order partial differential equations and the geometric understanding and construction of geometric integrator.

As expected, in this year, we were able to construct the geometric structure of arbitrary order variational differential equations, modelling the dynamics of physical phenomena that can be derived from variational calculus. For non-variational systems, we developed a modified formal Lagrangian formulation that allows us to formally construct a variational structure for any system of differential equations. As a first attempt, it was applied to the derivation of a structure-preserving numerical scheme for the viscous Burgers' equation.

Part of the results were presented at domestic and international conferences. The draft 'A modified formal Lagrangian formulation for general differential equations' (arXiv:2009.04102) has been under review for publication in a leading journal of applied mathematics. Several other manuscripts will be ready for submission soon.