On solving the nonlinear diffusion equation: A comparison of perturbation, iterative, and optimal techniques for an arbitrary diffusivity

Abstract

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.