ABSTRACT
This chapter develops an approximate proximal approach for 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. Considering such a context, along the text we develop an approximate numerical procedure of proximal nature applicable to a large class of models in physics and engineering. Finally, in the last sections, we present numerical examples and results related to a Ginzburg-Landau type equation.
