The main goals of the investigations by the laboratory are theoretical studies of convergence and stability of numerical methods for solving the Initial Value Problems for systems of SDE; construction of new families of stable numerical methods for solving SDE. Special attention is given to the development of new variable stepsize algorithms with automatic accuracy control for SDE, development of methods for the numerical analysis of stochastic oscillating and stiff systems, algorithms for the numerical estimation of unknown parameters of SDE.
An application software package is being developed for one of the most interesting applications of numerical methods for SDE in the financial mathematics, i.e. the analysis of dynamics of the market prices of stocks, bonds, options, futures and other assets. See Internet Guide on Financial Derivatives (in Russian cp-1251).
Another direction of investigations is the development of the user's interface for the algorithms of numerical mathematics, construction of the dialogue systems and an electronic manual.
The Dialogue system "Dynamics and Control" is created. It is designed for the numerical experiments when solving the problems of analysis and synthesis of automatic control of the dynamic objects. The dialogue system is created for the specialists in numerical mathematics, teachers in numerical mathematics and automatic control theory, and control systems designers.
The investigations of the laboratory are supported by the Russian Foundation of Fundamental Research under grant N 94-01-00074 "Numerical Analysis of Stochastic Differential Equations".