Existence and uniqueness, analytical solution, nonlinear differential equation, a priori estimation, a posteriori estimation.

The article presents a proof of the theorem of the existence and uniqueness of the analytical solution of the class of nonlinear differential equations of the third order, with a polynomial right-hand side of the sixth degree, in the complex domain. The class of the considered equations has been extended by means of a new change of variables. An a priori estimate of the analytical approximate solution is obtained. A variant of the numerical experiment of optimizing a priori estimates using a posteriori estimates is presented.

Viktor Nikolaevich Orlov, Dr. Phys. & Math. Sci., Associate Professor, Moscow State University of Civil Engineering, Moscow, Russia

Ludmila Vitaljevna Mustafina, Undergraduate, Moscow State University of Civil Engineering, Moscow, Russia