In this chapter we start to examine some techniques used for the numerical solution of partial differential equations (PDEs) and, in particular, equations which are special cases of the linear second-order equation with two independent variables $$a\frac{{{\partial ^2}u}}{{\partial {x^2}}} + b\frac{{{\partial ^2}u}}{{\partial x\partial y}} + c\frac{{{\partial ^2}u}}{{\partial {y^2}}} + d\frac{{\partial u}}{{\partial y}} + fu + g = 0$$ (6.1) where the coefficients a, b,..., g may be functions of x and y, but not of u.