Taylorian initial problem

ordinary differential equations, Taylor series, TKSL, MTSM

In recent years, intensive research in the field of numerical solutions of systems of ordinary and partial differential equations has been done at the Brno University of Technology, Faculty of Information Technology, Department of Intelligent Systems. The basic numerical method employed is the so-called Modern Taylor Series Method (MTSM). It has been described, studied, and numerous aspects have been investigated such as processing in parallel systems. Also a simulation system TKSL has been developed which is based on the Taylor series method.  Although there have been considerable practical results, theoretical issues are yet to be investigated. A theoretical background of the method, some succesful results, some comparisons to word standards and idea of parallel processing will be provided in this paper.