The Fast Implementation Of Compact Difference Scheme

Poisson equation and schrodinger equation play a key role in math and physics.Scientises have proposed a lot of ways to solve them.But with the rapid development of science and computer,efficient numerical solution is necessary.In this paper,a fast algorithm-sine transform is introduced which is based on the compact finite method combined with other discrete methods,such as time-splitting,cranknicolson to solve them.In order to understand the mentioned method more directly,we list some concrete examples,then solve them by the mentioned method.