APPLICATION OF THE ASYMPTOTIC ITERATION METHOD TO A SINGULARLY PERTURBED NONLINEAR SECOND-ORDER DIFFERENTIAL EQUATION

Using the Cauchy problem for a single nonlinear singularly perturbed second-order differential equation, we demonstrate the possibility of constructing approximations that converge to the exact solution in both the usual and asymptotic senses. The construction of the approximations and the proof of their convergence are based on the idea of ​​operator semi-inversion and the principle of contraction mappings.