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The solution of the mathematical model for flow in variably\udsaturated porous media described by the Richards equation (RE) is subject to\udheavy numerical difficulties due to its highly nonlinear properties and\udremains very challenging. Two different algorithms are used in this work to\udsolve the mixed form of RE: the traditional iterative algorithm and a\udtime-adaptive algorithm consisting of changing the time-step magnitude within\udthe iteration procedure while the nonlinear parameters are computed with the\udstate variable at the previous time. The Ross method is an example of this\udtype of scheme, and we show that it is equivalent to the Newton–Raphson\udmethod with a time-adaptive algorithm.  Both algorithms are coupled to different time-stepping strategies: the\udstandard heuristic approach based on the number of iterations and two\udstrategies based on the time truncation error or on the change in water\udsaturation. Three different test cases are used to evaluate the efficiency of\udthese algorithms.  The numerical results highlight the necessity of implementing an estimate of\udthe time truncation errors

Ross scheme, Newton–Raphson iterative methods and time-stepping strategies for solving the mixed form of Richards' equation