Construction of the Approximated Analytical Solutions for Nonlinear Ordinary Differential Equations Based on Application of Additional Boundary Conditions

Procedure of obtaining of the approximated analytical solutions for nonlinear ordinary differential equations of the first order is developed based on application of additional boundary conditions. The physical value of application of additional boundary conditions is found in solving the initial differential equation in the boundary points of a problem. Application of iterative method allows to solve this equation in the whole range of independent variable meanings and to receive analytical solutions of satisfactory accuracy by averaging the required unknown factors.