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Similarity reductions and similarity solutions for the generalized diffusion equation
Author(s) -
Moussa M. H. M.,
Abd AlHalim Zidan M.
Publication year - 2015
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3360
Subject(s) - mathematics , similarity (geometry) , diffusion equation , partial differential equation , similarity solution , ode , ordinary differential equation , diffusion , variety (cybernetics) , nonlinear system , differential equation , mathematical analysis , computer science , statistics , artificial intelligence , thermodynamics , physics , economy , boundary layer , quantum mechanics , economics , image (mathematics) , service (business)
Herein, the generalized diffusion equation that encompasses the nonlinear diffusion equation with a source term and the Boussinesq equation in hydrology as its particular form and appears in a wide variety of physical and engineering applications has been analyzed via symmetry method that was developed by Steinberg. According to physical situations, in each case, the similarity variables obtained have led us to an ordinary differential equation, and we acquire some new solutions by solving the ODEs. Copyright © 2015 John Wiley & Sons, Ltd