  New numerical method to calculate thermodynmic Bethe ansatz equations is
proposed based on Newton's method. Thermodynamic quantities of one-dimensional
Hubbard model is numerically calculated and compared with high temperature
expansion and numerical results of quantum transfer matrix method by J\"uttner,
Kl\"umper and Suzuki. The coincidence is surprisingly good. We get
high-temperature expansion of grand potential up to $\beta^6$.
