ABSTRACT
This chapter develops an improvement concerning the original format of the generalized method of lines. We recall that for the generalized method of lines, the domain of the partial differential equation in question is discretized in lines (or in curves) and the concerning solution is developed on these lines, as functions of the boundary conditions and the domain boundary shape. In this text, we introduce a slight change on the way we truncate the series solution generated through the application of the Banach fixed point theorem to obtain the relation between two adjacent lines. With such a new improvement, we have got very good results even as a typical parameter is too much small, decreasing substantially the numerical solution error for such a class of small parameters. In the last sections, we present numerical examples and results related to a Ginzburg-Landau type equation.
