In some cases relevant to engineering practice a material will be in an environment

where there is no convective transport – for example, pollutant released into a long

and narrow pipe with zero flow, or where heat may be diffusing along a metal wire

driven purely by temperature differences. In this case the equation reduces to:


where C is the concentration of the material or the temperature of the substance, x

is the axis, and K is the diffusion/dispersion coefficient. To solve this equation

using the finite difference method two steps are undertaken:

1. the solution space is digitised into a number of discrete points rather than a

continuum; and

2. the equation is approximated using standard approximations derived on the

basis of a Taylor expansion of the function.