Computer realization of variational methods for dissipative problems with nonclassical Hamilton’s actions

In the frame of the Euler’s functionals there may not exist solutions of the inverse problems of the calculus of variations, but if we extend the class of functionals then it could allow to get the variational formulations of given problems. There naturally arises the problem of the constructive determination of the corresponding functionals – nonclassical Hamilton’s actions - and their application for the search of approximate solutions of the given boundary value problems. The main goal of the paper is to demonstrate the opportunity of effective use of such functionals for the construction of approximate solutions with the high accuracy for the given dissipative problems.