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Two approaches to the calculation of approximate symmetry exemplified using a system of advection-diffusion equations. (English) Zbl 1102.65105
Summary: 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.

MSC:
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
76S05 Flows in porous media; filtration; seepage
80A20 Heat and mass transfer, heat flow (MSC2010)
35K55 Nonlinear parabolic equations
76M25 Other numerical methods (fluid mechanics) (MSC2010)
80M25 Other numerical methods (thermodynamics) (MSC2010)
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