On Numerical Challenge for the Distinction Between Smooth Functions and Analytic Functions

In the paper, we present numerical experiments for investigation of a property of functions.Especially, we focus on the smoothness.Two kinds of methods are used in numerical experiments.One is the interpolation and the other is the Cauchy problem for the Laplace operator.Numerical experiments are performed by using the spectral collocation method and a multiple-precision arithmetic.Numerical results show the possibility of the numerical computation for the distinction between smooth functions and analytic functions.