A correction for truncation errors associated with a finite-difference solution of the advection-dispersion equation with reaction is developed from a Taylor analysis. An explicit finite-difference scheme is used to show the effect of these truncation errors on the solution of an advection-dispersion equation with a first-order reaction term. The criteria for the stability of the finite-difference solutions are derived using a matrix method proposed by Smith (1978). Comparison with an analytical solution shows that the uncorrected errors are not negligible and that by correcting the finite-difference scheme for them the results will be more accurate. The approach can also be used for correcting other finite-difference schemes whenever they do not have second-order accuracy.