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

Journal of Computational and Applied Mathematics

Volumn 197, Issue 2, 2006, Pages 287-301

  Wiltshire, Ron ^a  

^a UNIVERSITY OF GLAMORGAN   (United Kingdom)

Author keywords

Advection diffusion systems; Approximate symmetry methods; Approximate symmetry reduction; Perturbation techniques

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; DIFFUSION; MOISTURE; PERTURBATION TECHNIQUES; POROUS MATERIALS;

ADVECTION-DIFFUSION SYSTEMS; APPROXIMATE SYMMETRY METHODS; APPROXIMATE SYMMETRY REDUCTION; SHAPE FUNCTIONS;

NONLINEAR SYSTEMS;

EID: 33747375134     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2005.11.003     Document Type: Article

References (9)

1. Baikov V.A., Gazizov R.K., and Ibragimov N.H. Approximate symmetries of equations with a small parameter. Mat. Sb. 136 (1988) 435-450 (English Transl. in: Math USSR Sb. 64(1989)427-441)
2. Baikov V.A., Gladkov A.V., and Wiltshire R.J. Lie symmetry classification analysis for nonlinear coupled diffusion. J. Phys. A 31 (1998) 7483-7499
3. De Vries D.A. Simultaneous transfer of heat and moisture in porous media. Trans. Amer. Geophys. Un. 39 (1958) 909-916
4. Fushchich W.I., and Shtelen W.M. On approximate symmetry and approximate solutions of the non-linear wave equation with a small parameter. J. Phys. A 22 (1989) L887-L890
5. Ibragimov N.H. New trends in theoretical developments and computational methods. CRC Handbook of Lie Group Analysis of Differential Equations vol. 3 (1996) 1-3
6. W.A. Jury, J. Letey, L.H. Stolzy, Flow of water and energy under desert conditions, in: Evans, Thames (Eds.), Water in Desert Ecosystems, Dowden, Hutchinson and Ross Inc., 1981.
7. Pakdemirli M., Yürüsoy M., and Dolapçi I.T. Comparison of approximate symmetry methods for differential equations. Acta Appl. Math. 80 (2004) 243-271
8. Philip J.R., and De Vries D.A. Moisture movement in porous media under temperature gradients. Trans Amer. Geophys. Un. 38 (1957) 222-232
9. Wiltshire R.J. Perturbed Lie symmetry analysis of systems of nonlinear diffusion equations. J. Nonlinear Math. Phys. 3 (1996) 130-138