Joint seminar of the Numerical Methods and Analysis Department of the Faculty of Mathematics and Informatics, Sofia University, and the Department of Mathematical Modelling and Numerical Analysis, IMI-BAS, will be held on September 13, 2019, Friday, at 11:00 am to 12:00 am in Room 403 of IMI-BAS.   Sen. Assistant Prof.  Dr. Ivan Hristov, Computer Informatics Department, FMI, and Prof. Dr. Zarif Sharipov from the IT Laboratory of the Joint Institute for Nuclear Research, Dubna, Russia, will deliver the following talks:  How to obtain a mathematically reliable long-term solution of a chaotic dynamical system?  Ivan Hristov  To obtain a mathematically reliable long-term solution of a chaotic dynamical system we have to be extraordinary in many directions. First, we have to use not the standard double [...]