Volume 9, Issue 1
Approximate Similarity Solution to a Nonlinear Diffusion Equation with Spherical Symmetry
DOI:

Int. J. Numer. Anal. Mod., 9 (2012), pp. 105-114

Published online: 2012-09

Preview Full PDF 270 1139
Export citation

Cited by

• Abstract

In this article we construct an approximate similarity solution to a nonlinear diffusion equation in spherical coordinates. In hydrology this equation is known as the Boussinesq equation when written in planar or cylindrical coordinates. Recently Li et al. [8] obtained an approximate similarity solution to the Boussinesq equation in cylindrical coordinates. Here we consider the same problem in spherical coordinates with the prescribed power law point source boundary condition. The resulting scaling function has a power law singularity at the origin versus a logarithmic singularity in the cylindrical case.

• Keywords

Approximate solutions similarity solutions Boussinesq equation nonlinear diffusion

34B15 35K20 76S05 80A20