The Saint-Venant—Picard—Banach method of integrating equations in partial derivatives with a small parameter
Abstract:
An iterative interpretation to the classical semi-inverse Saint-Venant method for constructing the solution of partial differential equations with a small parameter is given. The Picard operator uses for integrating the system of equations of the first order that enables us to obtain continuous integrals of first-order equations along the transverse coordinate of a narrow long strip. Verification of the boundary conditions on long edges yields equations for the slowly and rapidly changing components of the solution. The integrals of singularly perturbed equations for rapidly varying quantities are used to construct continuous solutions along the longitudinal coordinate according to Friedrichs. The solutions of the singularly perturbed equations describe the stress concentration with distributions functions.
