SCAIM Seminar: Andy Wan

Structure-preserving discretizations are numerical methods which can preserve important structures of differential equations at the discrete level. For systems with a Hamiltonian or variational structure, geometric integrators such as symplectic and variational integrators are a class of discretizations that can preserve symplectic structure, first integral, phase space volume or symmetry at the discrete level. In this talk, we present the multiplier method of constructing conservative finite difference schemes for ordinary and partial differential equations. The proposed discretization is shown to be consistent for any order of accuracy and that by construction, the discrete densities can be exactly conserved. In particular, the multiplier method does not require the system to possess a Hamiltonian or variational structure. Examples, including dissipative problems, are given to illustrate the method. This is joint work with Alexander Bihlo at Memorial University and Jean-Christophe Nave at McGill University.