SOLVING SYSTEMS OF STIFF ORDINARY DIFFERENTIAL EQUATIONS FROM MODEL OF BIOCHEMICAL REACTION NETWORKS USING IMPLICIT RUNGE -- KUTTA METHODS

Dynamic mathematical models in the form of systems of ordinary differential equations (ODEs) play an important role in systems biology. For any sufficiently complex model, the speed and accuracy of solving the ODEs by numerical integration is critical.Here we present an integration scheme that is based on Implicit Runge - Ktta Method and contains other unique features such as stiffly accurate. These features allow the integrator to take larger time steps than other methods. In practical applications, i.e. sy stems biology models of different sizes and behaviors, the method competes well with established integrators in solving the system equations, and it outperforms them significantly when function evaluation,accuracy and cpu time,is evaluated.