A kind regularization method with Poisson kernel to solve Cauchy problem of Schrödinger equation.

In this work, a precise regularization technique based on the mollification method is proposed to solve the ill-posed Schr $ \ddot {o} $ o ¨ dinger Cauchy problem with potential-free field. In the sense of Hadamard, this problem is severely ill-posed. Using the mollification regularization method based on Poisson kernel, some new error estimates are obtained under the priori and posteriori parameter selection rules. The regular approximate solutions are created, and the convergence evidences are provided. The good performance and high accuracy of this technique are demonstrated through various examples. The solution works well and is resistant to data disruption noise. [ABSTRACT FROM AUTHOR]