Research

Our research focuses on the computational study of stochastic differential-algebraic equations (SDAEs) and stiff stochastic differential equations (SDEs). These complex mathematical models are essential for understanding systems where random processes interact with algebraic constraints and stiff dynamics, such as in engineering, physics, finance, and biology. Our work includes several key areas:

Partitioning Methods: We develop efficient partitioning algorithms that decompose large, complex systems into smaller, more manageable sub-systems. This simplifies the computational analysis and enhances the accuracy and efficiency of simulations.

Stability Analysis: Investigating the stability properties of these equations is crucial for ensuring the reliability and robustness of the solutions. Our stability studies focus on identifying conditions under which solutions remain stable over time, even in the presence of randomness and stiff components.

Stochastic Study of Dynamic Complex Networks: We apply our expertise to the stochastic analysis of dynamic complex networks. This involves studying how randomness affects the behavior and evolution of interconnected systems such as biological networks, social networks, and communication networks. Understanding these dynamics helps in predicting and controlling system behavior under uncertainty.

Our cutting-edge research in these areas not only advances theoretical understanding but also provides practical solutions for real-world problems. We utilize state-of-the-art computational techniques and high-performance computing resources to tackle these challenges.

Click this link to browse through our research publications.