In this paper, we consider the Cauchy problem for the Laplace equation by group preserving
scheme (GPS) which is an ill-posed problem, because the solution does not depend continuously on
the data. For this, the Laplace equation, by using a semi-discretization method namely method of line, is
converted to an ODEs system and then obtained ODEs system is considered by GPS. Stability of GPS for
ill-posed Laplace equation is shown. The problem numerical results show the efficiency and power of
this method.