Upwinding in the method of lines

The method of lines (MOL) is a procedure for the numerical integration of partial differential equations (PDEs). Briefly, the spatial (boundary value) derivatives of the PDEs are approximated algebraically using, for example, finite differences (FDs). If the PDEs have only one initial value variable, typically time, then a system of initial value ordinary differential equations (ODEs) results through the algebraic approximation of the spatial derivatives.