The Method of Lines is a semi-analytical versatile tool for the solution of partial differential equations. For the analysis of spatial complex linear waveguide structures, this method is combined with impedance/admittance and field transformation, as well as with finite differences. This paper extends this approach to the treatment of structures with non-linear dielectric materials. The non-linear generalized transmission line equations are derived. An iterative algorithm based on the impedance/admittance transformation with the field transformation obtains efficient and self-consistent solutions. The specific limiting factors for the algorithm and how to overcome them were investigated. A bidirectional, spatially, and temporally periodic energy exchange between the harmonics were found. For demonstration, a stripe waveguide with the non-linear core is considered. The Kerr non-linearity was investigated, though the general case is treatable. The approach can be used for any spatial structure, including, for instance, photonic crystal waveguides and metamaterials.