论文信息 - An improved and generalized second order, unconditionally positive, mass conserving integration scheme for biochemical systems

An improved and generalized second order, unconditionally positive, mass conserving integration scheme for biochemical systems

Bruggeman et al. [J. Bruggeman, H. Burchard, B. Kooi, B. Sommeijer, A second-order, unconditionally positive, mass-conserving integration scheme for biochemical systems, Applied Numerical Mathematics 57 (1) (2007) 36-58] presented novel first and second-order implicit integration schemes which guarantee both conservation (in a strict biochemical sense) and positive-definite results (hereafter, BBKS1 and BBKS2 respectively). In this paper we show that it is possible to achieve substantially more accurate results by making a minor modification to the BBKS-schemes (hereafter, we refer to the revised first- and second-order schemes as mBBKS1 and mBBKS2). The BBKS and the mBBKS schemes are shown to be special cases of a more generalized scheme (dubbed gBBKS). All operate by automatically slowing the forecaster time-step-averaged reaction rates in order to maintain positivity. The mBBKS scheme induces less slowing than the BBKS one. With a second modification, gBBKS-type schemes can become unusual adaptive-time-step schemes. Unfortunately, for the ODE-systems that we examined, the adaptive-mBBKS variant proves to be substantially less efficient than standard adaptive schemes (in this instance, adaptive time-step second-order explicit Runge-Kutta). Nonetheless, it is possible that the adaptive-mBBKS-scheme would become more competitive when the right-hand sides of a system of ODEs are more expensive to evaluate.

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