Shornikov Y.V.   Dostovalov D.N.   Denisov M.S.  

Features of the numerical simulation of hybrid systems by ISMA

Reporter: Shornikov Y.V.

This paper is devoted to the efficient numerical analysis and specification of high-dimensional hybrid systems in the ISMA software.
Correct detection of state change is an important problem in the hybrid systems modeling. The proposed algorithm for selecting the integration step takes into account the dynamics of event functions as well as precision and stability of numerical scheme. The original method of the switching points localization is based on the special theorem proved. A typical two-tank system is considered to demonstrate the algorithm efficiency. Results of computer experiments demonstrate the justifiability of the proposed algorithm.
Another important task is the simulation of high-dimensional stiff hybrid systems. A model of radiolabeled antibodies penetration in tumor-bearing tissue is considered as an example. Computer analysis results have shown the efficiency of the original explicit methods of variable order and the step with stability control and semi-explicit (m,k)-methods for solving high-dimensional stiff tasks.
Also it is shown, that the use of implicit methods for hybrid systems integration without event-function dynamics leads to wrong global solution. ISMA program modules specification problem is considered over the necessity of algorithmic composition of right-hand member of the high-dimensional differential task.