Adaptive Methods For Stochastic Simulation Of Biochemical Systems

Computational and Systems Biology are recently experiencing a rapid development. Mathematical modeling is a key tool in analyzing critical biological processes in cells and living organisms. In particular, stochastic models are essential to accurately describe the biochemical processes in the cell. However, stochastic models are computationally much more challenging than the traditional deterministic models. Also, the sheer scale of biological processes makes efficiency of the simulation a key issue. In this thesis we study the numerical solution of a continuous stochastic model of biochemical systems, the Chemical Langevin Equation. We propose an adaptive step-size method for the Euler-Maruyama scheme applied to small noise problems. The adaptive technique is p-mean convergent and computes simultaneously all the trajectories, using the same time-step on all trajectories. Our adaptive algorithm is tested on several examples arising in applications and shown to perform much better than the fixed step-size schemes.