A highly accurate and effective scheme for solving the time-dependent Schrodinger equation is implemented using Mathematica. The present code achieves a precision of one part in 10(17), which is found to be independent of time steps. With a new wavefunction splitting algorithm and a more efficient method for evaluating transmission coefficients, the improved code requires considerably less CPU time than that reported in our previous publication (Wang and Scholz, Phys. Rev. A 57 (1998) 3554). (C) 2001 Elsevier Science B.V. All rights reserved.