Resumen de Group preserving scheme for the Cauchy problem of the Laplace equation

Saeid Abbasbandy, M.S. Hashemi

• 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.