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Although based on exact analytical solutions, semi-analytical solute transport models can have significant numerical error in applications with high frequency oscillatory source terms and when parameter value combinations cause series solution approximations to converge slowly. Methods for correcting these numerical errors are presented and implemented in the AT123D code, which employs Green's functions to represent point, linear, and rectangular prismatic source zones. In order to increase its computational accuracy, a Romberg numerical integration scheme was added to AT123D with prespecified error criteria, variable time stepping, and partitioning of the integral to handle rapidly changing source terms. More rapidly converging series solution approximations for the Green's functions were also incorporated to improve both accuracy and computational efficiency for finite-depth aquifers. AT123D also has been modified to eliminate redundant calculations at points where approximate steady-state conditions have been reached to improve computational efficiency during numerical integration. These modifications help to decrease computer run times that can be excessive for three-dimensional problems with large numbers of computational points, small time steps, and/or long simulation time periods. Errors in the original AT123D code also were corrected in this modified version, AT123D-AT, in order to accurately simulate finite-duration (pulse) source releases.