I have to find difference between ADI method on solving 2D diffusion equation with larger time-step and also 2D steady-state diffusion equation using centered difference method with smaller time-step. The boundary is Dirichlet.

Can anyone explain to me what the difference between this two?
here i attached the result i got from those methods. numerical and analytical solution for steady state diffusion (laplace) produce same answer without error.

  
 

Numerical solution ulx.t) of Laplace Eq 00 01 02 03 05 00 8 8 8 8 8 w render in the Pits pane by defasit. To ale thee alser inte in the sale, anche e di Pieting