Numerical approximation of the potential in the two-dimesional inverse scattering problem

Juan Antonio Barceló, Carlos Castro, Juan Manuel Reyes

Type: Article

Publication Date: 2015-12-10

Citations: 12

DOI: https://doi.org/10.1088/0266-5611/32/1/015006

Abstract

We present an iterative algorithm to compute numerical approximations of the potential for the Schr\"odinger operator from scattering data. Four different types of scattering data are used as follows: fixed energy, fixed incident angle, backscattering and full data. In the case of fixed energy, the algorithm coincides basically with the one recently introduced by Novikov in [Novikov, R. G., "An iterative approach to non-overdetermined inverse scattering at fixed energy", Sbornik: Mathematics 206 (1), 120-134 (2015)], where some estimates are obtained for large energy scattering data. The numerical results that we present here are consistent with these estimates.

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