Approximation of the inverse scattering Steklov eigenvalues and the inverse spectral problem

In this paper, we consider the numerical approximation of Steklov eigenvalue problem that arises in inverse acoustic scattering. The underlying scattering is for an inhomogeneous isotropic medium. These eigenvalues have been proposed to be used as a target signature since they can recovered from data. A Galerkin method studied where basis functions are Neumann eigenfunctions Laplacian. Error estimates and proven by appealing Weyl’s law. We will test against separation variables order validate theoretical convergence. also spectral estimating/recovering refractive index knowledge eigenvalues, monotone with respect real-valued implying nondestructive testing. Some examples provided problem.