RESUMEN
A two-step hybrid perturbation
Galerkin technique for solving a variety of applied mathematics problems
involving a small parameter is presented. The first step consists of using a
regular or singular perturbation method to determine the asymptotic
expansion of the solution in terms of the small parameter. Then the approximate
solution is assumed to have the form of a sum of perturbation coefficient
functions multiplied by (unknown) amplitudes (gauge functions). In the second
step the classical Bubnov–Galerkin method is used to
determine these amplitudes. The resulting hybrid method has the potential of
overcoming some of the drawbacks of the perturbation and Bubnov–Galerkin
methods applied separately, while combining some of the good features of both. The
proposed method is applied to some singular perturbation problems in slender
body theory. The results obtained from the hybrid method are compared with
approximate solutions obtained by other methods, and the applicability of the
hybrid method to broader problem areas is discussed.