By Erwan Faou
The target of geometric numerical integration is the simulation of evolution equations owning geometric houses over lengthy sessions of time. Of specific value are Hamiltonian partial differential equations commonly coming up in software fields corresponding to quantum mechanics or wave propagation phenomena. They convey many vital dynamical positive factors akin to strength upkeep and conservation of adiabatic invariants over lengthy sessions of time. during this environment, a average query is how and to which volume the copy of such long-time qualitative habit may be ensured by way of numerical schemes. ranging from numerical examples, those notes supply a close research of the Schrödinger equation in an easy atmosphere (periodic boundary stipulations, polynomial nonlinearities) approximated via symplectic splitting tools. research of balance and instability phenomena brought on through area and time discretization are given, and rigorous mathematical factors are supplied for them. The e-book grew out of a graduate-level path and is of curiosity to researchers and scholars looking an creation to the subject material. A booklet of the eu Mathematical Society (EMS). disbursed in the Americas through the yankee Mathematical Society.
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