Central difference regularization method for the Cauchy problem of the Laplace's equation

In this paper, we consider the Cauchy problem for the Laplace's equation where the Cauchy data is given at x = 0 and the solution is sought in the interval 0 < x < 1. A semi-discrete difference schemes together with a choice of regularization parameter is presented and error estimate is obtained. A numerical example shows that the method works effectively.