The stability conditions of finite difference schemes for schr#xF6;dinger, Kuramoto#x2010;Tszuki and heat equations

摘要

We consider various finite difference schemes for the first and the second initial#x2010;boundary value problems for linear Kuramoto#x2010;Tsuzuki, heat and Schr#xF6;dinger equations ind#x2010;dimensional case. Using spectral methods, we find the conditions of stability on initial data in theL2norm.