Stability Issues in Computation of Stiff Stochastic Differential Equation Systems
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The proposed project plans to investigate the difficulties in simulation, in terms of efficiency of computational methods and their stability and their ability to elucidate the time scales involved, the behaviour of stiff stochastic differential equation systems. Stiff stochastic differential equations (SDEs) arise in variety of physical models, for example, in models of on-chip mechatronic systems and in biochemical reaction systems of intra-cellular pathways.
Loosely speaking, large changes in the solution of SDE in short (relative to the simulation interval) time sub-intervals is construed as stiffness. The difficulty with stiff SDEs arises from the two time scales inherent in SDEs and the stiffness in the diffusion coefficients gives rise to numerical stability issues different from deterministic differential equations. While stability of computation of deterministic stiff differential equations have been studied for a long time in much detail, such studies for stiff SDE systems are new as the extension of tools and methods for stiff deterministic differential equations to stiff SDEs is non-trivial.
The proposed project will involve the following research issues: (1) Characterization of stiffness in stochastic differential equation systems in terms of time scales and computational difficulties involved. (2) Computational stability analysis of SDE systems. (3) Numerical methods applied to solve stiff SDEs: Stability and its relationship to efficiency, error and stepsize control and sensitivity to perturbation.