New Trends in Taylor Series Based Computations

Motto: For the derivatives of all decent functions analytic formulas can be found but with integration this is only true for very special decent functions. The aim of our paper is to describe a new modem numerical method based on the Taylor Series Method and to show how to evaluate the high accuracy and speed of the corresponding computations. It is also the aim of our paper to show how to calculate finite integrals that are the fundamental part in signal processing, especially in Fourier analysis and how to use it for symbolic operations. It is a fact that the accuracy and stability of the algorithms we have designed significantly exceeds the presently known systems. In particular, the paper wants to concentrate, using the previous results and latest development trends, on the simulation of dynamic systems and on extremely exact mathematical computations.