We propose a practical implementation of high-order fully implicit<br />
Runge-Kutta(IRK) methods in a multiple precision floating-point environment.<br />
Although implementations based on IRK methods in an IEEE754 double precision<br />
environment have been reported as RADAU5 developed by Hairer and SPARK3<br />
developed by Jay, they support only 3-stage IRK families. More stages and<br />
higher-order IRK formulas must be adopted in order to decrease truncation<br />
errors, which become relatively larger than round-off errors in a multiple<br />
precision environment. We show that SPARK3 type reduction based on the<br />
so-called W-transformation is more effective than the RADAU5 type one for<br />
reduction in computational time of inner iteration of a high-order IRK process,<br />
and that the mixed precision iterative refinement method is very efficient in a<br />
multiple precision floating-point environment. Finally, we show that our<br />
implementation based on high-order IRK methods with embedded formulas can<br />
derive precise numerical solutions of some ordinary differential equations.