The proposed research is focused on a new computational method developed for solving variational problems with a large, possibly infinite, set of constraints. An investigation of various aspects of this method is proposed, with emphasis on the error analysis, discretization techniques, generalizations and convergence acceleration. On the basis of this method computational algorithms are expected to be developed for a class of equilibrium and slow evolution problems and for evolution problems with a large number of conservation laws. A large class of applications in physics and engineering is proposed for the investigation with the help of these computational algorithms. Applied problems include problems in ideal magnetohydrodynamics (tokamak design, analysis of the experimental data), fluid dynamics (design of efficient computational algorithms with improved convergence and stability properties) and astrophysics. The variational approach is also proposed for developing numerical methods for finding periodic solutions of nonlinear wave equation and quasi-periodic solutions of second order dynamical systems.
