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impossible to obtain. The nonlinearity of equations (6) and (7), and
the typical variable boundary conditions, have led to the use of
numerical methods to solve practical problems of soil-plant-water
relationships, such as irrigation management for agricultural crops.
For one-dimensional flow, equation (6) has been successfully solved
using explicit finite difference methods by many researchers. Hanks and
Bowers (1962) developed a numerical model for infiltration into layered
soils. They solved the Richards equation for the hydraulic potential
using implicit finite difference equations with a Crank-Nicholson
technique which averages the finite differences over two successive time
steps. Rubin and Steinhardt (1963) developed a numerical model to study
the soil water relationships during rainfall infiltration. They used a
Crank-Nicholson technique to solve Richards equation for the water
content. Rubin (1967) developed a numerical model which analyzed the
hysteresis effects on post-infiltration redistribution of soil water.
Haverkamp et al. (1977) reviewed six numerical models of one-
dimen s torra. 1 infiltration. Each model employed different discretization
techniques for the nonlinear infiltration equation. The models reviewed
were solved using both the water content based equation and the water
potential based equation. They found that implicit models which solved
the potential based infiltration equation had the widest range of
applicability for predicting water movement in soil, either saturated or
nonsaturated.
Clark and Smajstrla (1983) developed an implicit model of soil
water flow to study the distribution of water in soils as influenced by
various irrigation depths and intensities. The model simulated water
application rates from center-pivot irrigation systems with intensities