Additive operator splitting methods for solving systems of nonlinear finite difference equations

There exists a considerably body of literature on the development, analysis and implementation of multiplicative and additive operator splitting methods for solving large and sparse systems of finite difference equations arising from the discretization of partial differential equations. In this note, we will review the Newton-Arithmetic Mean and the Modified Newton-Arithmetic Mean methods for solving nonlinear and weakly nonlinear systems of difference equations arising from the discretization of diffusion-convection problems