CONSTRUCTION OF THE ASYMPTOTIC OF THE SOLUTION OF A SINGULARLY PERTURBED PARTIAL DIFFERENTIAL EQUATION WITH A SPECIAL LIN

Abstract

This article is devoted to the construction of asymptotic of the solution a singularly perturbed equation in private derivatives - of the Carrer’s equation. It should be noted that the the Carrer’s equation under consideration has a special line and is considered in the rectangular region. It is impossible to determine the exact solution of the majority of tasks of applied mathematics, hydrodynamics, physics due to complex boundary conditions and nonlinearity. To construct asymptotic, a classic asymptotic method was used - the perturbation method. Based on this method, the approximate solutions of both linear and nonlinear differential equations, and equations in private derivatives can be relatively easily. The efficiency of using this method is achieved by the localization of the interval under consideration, i.e. the result will be more accurate than the surrounding area. The classic method is very well applicable for tasks considered in rectangular areas.