NEW ALGORITHM OF REDUCTION OF THE TWO-DIMENSIONAL EQUATION OF ELLIPTIC TYPE TO A CANONICAL FORM
The main objective of the work to give researchers using partial differential equations of elliptic type, the ability to fairly simple and reliable way to bring the equation to the form, where it is present the main part of the Laplace operator. Unlike the known the algorithm of reduction of the equation of elliptic type to a canonical form which doesn’t demand transition to complex area is earlier offered. For realization of this algorithm it is necessary to solve the ordinary differential equation which is simpler than the characteristic equations in a hyperbolic case. The solution of the problem is reduced to an algorithm for constructing solutions of the system of ordinary differential equations of the form rather simple and is carried out in the source area in the plane of the real variables.