Similarity solution of the Boussinesq equation
نویسندگان
چکیده
Similarity transforms of the Boussinesq equation in a semi-in®nite medium are available when the boundary conditions are a power of time. The Boussinesq equation is reduced from a partial dierential equation to a boundary-value problem. Chen et al. [Trans Porous Media 1995;18:15±36] use a hodograph method to derive an integral equation formulation of the new dierential equation which they solve by numerical iteration. In the present paper, the convergence of their scheme is improved such that numerical iteration can be avoided for all practical purposes. However, a simpler analytical approach is also presented which is based on ShampineÕs transformation of the boundary value problem to an initial value problem. This analytical approximation is remarkably simple and yet more accurate than the analytical hodograph approximations. Ó 2000 Elsevier Science Ltd. All rights reserved.
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