Numerical investigations methods for quantum systems with many degrees of freedom, based on approximate functional integration approach is elaborated. The thermodynamic characteristics of three-dimensional Bose gas are studied. The computation algorithm of functional integrals appearing in this problem, including particle identification and wave function symmetry principles is created . A numerical method for the inverse problem of quantum scattering theory is suggested. It is based on two asymptotic regulations: the first one uses the asymptotic behaviors of the phase shift and of the Jost function module for high energies, and the second one - the by step asymptotic discretisation of the reciprocals to "almost" Toeplitz and Hankel matrices. The last one permits to avoid the unstable procedure of numerical differentiation .
A new quantization condition for asymptotic momenta of decay products of a resonance was obtained . The mathematical statements of boundary Schwinger-Dyson and Bethe-Salpeter problems for some quark potential QCD models and the QCD-inspired quarkonium model at finite temperature are proposed. An algorithm for numerical investigation is constructed and numerical analysis of models is performed . The LLP-equations in bipolaron theory have been solved numerically . The numerical modeling of the dynamics of gas motion with account of active surface has been performed . Algorithms, software and numerical study of some muon catalyzed fusion processes and exotic atoms have been presented on International Symposium mu CF-95, Dubna, 1995. Algorithms and software for computing of quasielastic scattering parameters of some light exotic nuclei are created . Numerical investigation of the resonance phenomena in subatomic physics has been performed . Software and numerical study of the quasiparticle- phonon nuclei model has been done .