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Zbl 1102.65105
Wiltshire, Ron
Two approaches to the calculation of approximate symmetry exemplified using a system of advection-diffusion equations. (English)
[J] J. Comput. Appl. Math. 197, No. 2, 287-301 (2006). ISSN 0377-0427

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 2000:: *65M70 Spectral, collocation and related methods (IVP of PDE)
76S05 Flows in porous media
80A20 Heat and mass transfer
35K55 Nonlinear parabolic equations
76M25 Other numerical methods
80M25 Other numerical methods

Keywords: approximate symmetry methods; approximate symmetry reduction; perturbation techniques; advection-diffusion systems; heat transport; moisture transport; flows in porous media; Lie group method

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Zentralblatt MATH Berlin [Germany]