A hybrid Perturbation-Galerkin technique that combines multiple expansions

A two-step hybrid perturbation-Galerkin method for the solution of a variety of differential equations-type problems is found to give better results when multiple perturbation expansions are employed. The method assumes that there is a parameter in the problem formulation and that a perturbation method can be used to construct one or more expansions in this parameter. An approximate solution is constructed in the form of a sum of perturbation coefficient functions multiplied by computed amplitudes. In step one, regular and/or singular perturbation methods are used to determine the perturbation coefficient functions. The results of step one are in the form of one or more expansions, each expressed as a sum of perturbation coefficient functions multiplied by a priori known gauge functions. In step two, the classical Bubnov–Galerkin method uses the perturbation coefficient functions computed in step one to determine a set of amplitudes that replace and improve upon the gauge functions. The hybrid method has ...