A Hybrid Perturbation Galerkin Technique with Applications to Slender Body Theory

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 broade...