Many direct and inverse problems in hydrology re quire the efficient solution of parabolic partial differential equations which are characterized by stiffness and numerical dispersion. An optimal method for solving such equations uses the method of lines to discretize the spatial variables and a finite-difference scheme to discretize time. This method is asymptotically stable and minimizes the global error caused by discretization of time. The numerical performance of the method has been evaluat ed on test problems that realistically simulate aquifers.
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