[en] The solution to the finite element matrix differential equations resulting from the discretization of the contaminant transport equation is normally obtained by a finite difference (Crank-Nicolson) approximation to the time derivative. The total computational effort is then directly related to the number of unknowns and the number of time steps required to obtain accurate and stable solutions. An alternative is the Arnoldi algorithm, which is a type of Rayleigh-Ritz method for reduction of the matrix differential system to a much smaller system. The small system is solved by the standard Crank-Nicolson algorithm with very little computational effort. A matrix vector multiplication is then used to obtain the original solution at desired time steps. By means of examples, it is shown that the Arnoldi algorithm affords an efficient means of solving large finite element models of contaminant transport. (Author) (4 refs., 4 figs., 3 tabs.)