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On solving the nonlinear diffusion equation: A comparison of perturbation, iterative, and optimal techniques for an arbitrary diffusivity
Author(s) -
Parlance J.Y.,
Babu D. K.
Publication year - 1977
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr013i001p00213
Subject(s) - thermal diffusivity , perturbation (astronomy) , iterative method , nonlinear system , mathematics , mathematical analysis , mathematical optimization , physics , thermodynamics , quantum mechanics
A recent solution determined by Babu for an arbitrary soil‐water diffusivity is compared with two earlier solutions. It is shown that the perturbation solution is identical to the iterative result when Cisier's (1974) correction is used. It is also shown that a result obtained by optimization, which is numerically indistinguishable from either the perturbation or iterative result, has a much simpler analytical form.