Computational modelling of potential and resonant scattering for short range and Coulomb potentials was investigated in this study. The resonant scattering problem is formulated with the short range potential composed of a spherically symmetric square well and spherically symmetric square barrier. An iteration scheme of a continuous analogue of the Newton method for continuous spectral problem with correct asymptotic in uncoupled partial waves has been developed. The nonlinear representation of the scattering problem for the normalized radial Schrödinger equation is solved numerically using the difference sweep technique. The second order accuracy scheme developed allow to find scattering phases and wave functions as well as investigate their numerical evolution. The scattering phases and wave functions dependence on the scattering problem parameters have been studied.