A recursive formulation of Galerkinʹs method in terms of the tau method: Bounded and unbounded domains

The recursive formulation of the Tau Method (see [1,2]) is used to simulate the method of Galerkin. As a result of this, a new recursive formulation of Galerkinʹs Method is deduced. Furthermore, it is shown that the Galerkinʹs Method is a special form of a Tau Method with a weighted polynomial basis. Examples of application to the numerical approximation of linear and nonlinear partial differential equations, defined on bounded and unbounded domains, are also given.