Although Pade presented his fundamental paper at the end of the last century, the studies on Pade's approximants only became significant in the second part of this century.Pade procedure is related to the theory of continued fractions, and some convergence theorems can be expressed only in terms of continued fractions. Further, Pade approximants have some advantages of practical applicability with respect to the continued-fraction theory. Moreover, as Chisholm notes, a given power series determines a set of approximants which are usually unique, whereas there are many ways of writing an associated continued fraction.The principal advantage of Pade approximants with respect to the generating Taylor series is that they provide an extension beyond the interval of convergence of the series.Pade approximants can be applied in many parts of fluid-dynamics, both in steady and in nonsteady flows, both in incompressible and in compressible regimes.This book is divided into four parts. The first one deals with the properties of the Pade approximants that are useful for the applications and illustrates, with the aid of diagrams and tables, the effectiveness of this technique in the field of applied mathematics. The second part recalls the basic equations of fluid-dynamics (those associated with the names of Navier-Stokes, Euler and Prandtl) and gives a quick derivation of them from the general balance equation. The third shows eight examples of the application of Pade approximants to steady flows, also taking into account the influence of the coupling of heat conduction in the body along which a fluid flows with conduction and convection in the fluid itself. The fourth part considers two examples of the application of Pade approximants to unsteady flows.
Part 1 Pade' approximants: elements of Pade' approximants theory; some theoretical aspects of Pade' approximants. Part 2 The fluid-dynamic equations: balance equations; inner-outer expansions. Part 3 Some examples of application of Pade' approximants in steady flows: the thermo-fluid-dynamic equations; flows over bodies in forced convection - the flat plate case; forced convection in stagnation flow; appendix - motion equations in the odograph plane; flows over bodies in forced convection - the wedge case; the coupling of conduction with laminar natural convection along a vertical flat plate; variable-properties effects - free convection, plane jet in a moving medium. Part 4 Some examples of application of Pade' approximants in unsteady flows: the impulsively started flow away from a plane stagnation-point; the impulsively started flow past a circular cylinder.