Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia8828Research ArticleOn Numerical Solution of Direct and Inverse Scattering Problems for Spherically Symmetric Potentials Dependingon ParametersPuzyninaT PLaboratory of Information Technologiespuzynina@jinr.ruThachVo TrongLaboratory of Information Technologiesvotrongthach@jinr.ruJoint Institute for Nuclear Research150420124738608092016Copyright © 2012,2012The scattering problem for the radial Schr̈odinger equation, in contrast to a statement of Cauchy’s problem, is formulated as a boundary value problem for a wave function with a non-linear asymptotic condition with exclusion of an unknown phase shift. The phase shift is determined after calculation of the wave function by taking into account its asymptotic behavior and applying the iteration schemes of a continuous analog of Newton’s method (CANM). The inverse problem for an equation with a potential depending on the parameters is reduced to minimization problem with respect to the parameters for the functional that describes the sum of squares of deviations of the speciﬁed values of phase shifts from the corresponding calculated values. Basic features of the computational schemes are demonstrated by solution of the problem with Morse’s potential which admits analytical solution and also by solving the problem with Woods–Saxon’s potential.Schr¨odinger equationscattering problemnon-linear boundary value problemiterations of CANMpotentialsparametersinverse problemfunctionalminimizationуравнение Шрёдингеразадача рассеяниянелинейная граничная задачаитерации НАМНпотенциалыпараметрыобратная задачафункционалминимизация