Momentum conservation law in time evolutions of PDEs by the energy preserving numerical methods

Sasa, Narimasa  

In accordance with the basic research for the material development, we develop a numerical scheme for large scale parallel numerical simulation of a quantum condensate. The energy conserving numerical scheme simultaneously satisfies the conservation of the momentum of the system. We prove the conservative property of the numerical scheme theoretically and numerically. We also demonstrate that the conserved quantity stay a constant more accurate than ever before by performing numerical simulations.