Padé Approximation to Solve the Problems of Aerodynamics and Heat Transfer in the Boundary Layer

In this chapter, we describe the applications of asymptotic methods to the problems of mathematical physics and mechanics, primarily, to the solution of nonlinear singular perturbed problems. We also discuss the applications of Padé approximations for the transformation of asymptotic expansions to rational or quasi-fractional functions. The applications of the method of matching of internal and external asymptotics in the problem of boundary layer of viscous gas by means of Padé approximation are considered.