One-dimensional numerical simulation is carried out in order to obtain growth rates at several temperature gradients. The simulation agrees well with experimentally obtained concentration profiles in solid. From numerical results, it is found that a growth rate is almost proportional to the temperature gradient in a low temperature-gradient region as the one-dimensional traveling liquidus-zone (TLZ) theoretical model predicts. However, the growth rate becomes slightly higher than the theoretically predicted one in high temperature-gradient region. On the other hand, the growth rate is almost proportional to solute concentration gradients in the whole range. These results indicate that the TLZ method is one of solution growth techniques. It is found that the TLZ method precisely predicts the spontaneous growth rate, within an error of 3% in the region of the low temperature-gradient. (C) 2004 Elsevier B.V. All rights reserved.