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Some Accurate Numerical Solutions of the Soil-Water Diffusion Equation¹

ABSTRACT

Some accurate numerical solutions are obtained for the soil-water diffusion equation. The method replaces the two endpoint boundary value problem with a standard initial value problem and uses iteration to select the appropriate initial slope. The results obtained are accurate to seven significant figures and the solution exhibits a wetting front with a sharp corner and foot at the leading edge of the front. The corner and foot highlights our ignorance of the processes by which water percolates the soil at low concentrations.

¹ This research was carried out at Griffith University, with the support of University Research Grant no. 35-0600.

² Senior Lecturer in Numerical Methods, and Professor of Applicable Mathematics, respectively, Australian Environmental Studies, Griffith Univ., Nathan, 4111, Australia.

Received for publication July 11, 1979. Accepted for publication December 3, 1979.