High Order Numerical Integration Method and its Applications – The First 36 Years

The aim of this paper is to remember the work of our colleague Jiří Kunovský. The high order integration method that he developed with his students and colleagues has many positive properties and is studied to this day. The paper shows these properties on a set of technical initial value problems. The MATLAB implementation of Modern Taylor Series Method is compared with state-of-the-art MATLAB solvers.