Geometric methods of solving boundary-value problems

Abstract

In this paper, we list several geometrical methods of solving the boundary problems for equations of the mathematical physics.Constructing solutions invariant w.r.t. symmetries of the problem is discussed. A method based on the representation of the equation at hand in the evolutionary form is pointed out. The methods based on the deformation of the boundary problem along discrete or continuous parameters are described. Among these methods,we note the direct iterations, the boundary conditions homotopy,the relaxation method,and the deformation of the initial equation.Then, comparative analysis of the results of computer experiments in applying these methods is carried out.