Stability of 2D ADI method. 0<x<π and 0<y<π are dimensionless wavenumbers. n=dt*kappa/dx^2 is dimensionless timestep.

z is the eigenvalue for one timestep. The timestep consists of one half step [implicit x, explicit y] + one half step [implicit y, explicit x].

z=[[1-n]^2+[1-n]*n*[cos([x])+cos([y])]+n^2*cos([x])*cos([y])]/[[1+n]^2-([1+n]*n*[cos([x])+cos([y])])+n^2*cos([x])*cos([y])]

abs(x)>pi

abs(y)>pi

Graph of the formula

This file was created by Graphing Calculator 3.5.
Visit Pacific Tech to download the helper application to view and edit these equations live.