  In this work we propose an efficient parallelization of multiple-precision
Taylor series method with variable stepsize and fixed order. For given level of
accuracy the optimal variable stepsize determines higher order of the method
than in the case of optimal fixed stepsize. Although the used order of the
method is greater then that in the case of fixed stepsize, and hence the
computational work per step is greater, the reduced number of steps gives less
overall work. Also the greater order of the method is beneficial in the sense
that it increases the parallel efficiency. As a model problem we use the
paradigmatic Lorenz system. With 256 CPU cores in Nestum cluster, Sofia,
Bulgaria, we succeed to obtain a correct reference solution in the rather long
time interval - [0,11000]. To get this solution we performed two large
computations: one computation with 4566 decimal digits of precision and 5240-th
order method, and second computation for verification - with 4778 decimal
digits of precision and 5490-th order method.
