Two approaches to the calculation of approximate symmetry exemplified using a system of advection–diffusion equations

Two algorithms used to evaluate the approximate symmetries of nonlinear systems are compared from a theoretical view point. The two quite distinct algorithms are cast into a form where one method can clearly be seen to be more general than the second. The circumstances for the equivalence of the two methods are presented and for these cases it is shown how the approximate symmetries found by one method may easily be calculated for the second. These ideas are exemplified by calculating new approximate symmetry reductions for a systems of advection–diffusion equations that describe the simultaneous transport of heat, moisture and solute in porous media and which contain unknown shape functions.