Applications of Newton-Type Iterations for Computational Physics

Methods of computational physics developed for investigating models of complex physical processes in different fields of theoretical physics are considered. A general mathematical formulation of equations for the models under study is given, and numerical methods are described. Within the quantum mechanical few-body system, the following problems are considered in the adiabatic representation: calculations of bound and semi-bound state energies and scattering matrices of three bosons on a straight line with zero radius pair interactions, high-precision calculation of the ground state energy of the helium atom, calculations of multiple differential cross sections for the ionization processes of the ground state of the helium atom by fast electrons and protons, calculations of the ground state energies (including metastable state energies) of the beryllium dimer and high-precision calculation of the ground state energy of the Dirac electron in the field of two-center Coulomb field. The results of their numerical study are presented and compared with the results of other authors and some experimental data.