  Time-dependent Partial Differential Equations with given initial conditions
are considered in this paper. New differentiation techniques of the unknown
solution with respect to time variable are proposed. It is shown that the
proposed techniques allow to generate accurate higher order derivatives
simultaneously for a set of spatial points. The calculated derivatives can then
be used for data-driven solution in different ways. An application for Physics
Informed Neural Networks by the well-known DeepXDE software solution in Python
under Tensorflow background framework has been presented for three real-life
PDEs: Burgers', Allen-Cahn and Schrodinger equations.
