New efficient algorithm for solving thermodynamic chemistry
New efficient algorithm for solving thermodynamic chemistry
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求解热力学化学的新高效算法
DOI：
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
P. Behra
中科院分区：
文献类型：
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作者：
J. Carrayrou;R. Mosé;P. Behra
使用最常用的牛顿-拉夫森方法对复杂非线性化学系统的热力学平衡进行建模可能会导致不收敛。根据方程组的数学性质，定义了化学上允许的区间。通过施加这个间隔，牛顿-拉夫森方法的鲁棒性以较低的计算时间成本得到提高。新方法，即正连续分数，不依赖于目标函数的一阶导数来求解。因此，通过将这种非常鲁棒的方法与快速牛顿拉夫森方法以及化学允许区间的定义相结合，建立了一种新算法。这种组合算法在可靠性、鲁棒性和速度方面非常令人印象深刻。
Modeling thermodynamic equilibrium of complex nonlinear chemical systems with the most used Newton-Raphson method can lead to nonconvergence. From the mathematical properties of the set of equations, a chemically permitted interval is defined. By imposing this interval, the robustness of the Newton-Raphson method is increased at a low computing time cost. The new method, the positive continuous fraction, does not depend on the first derivative of the objective function to find the solution. A new algorithm is thus built by the association of this very robust method with the fast Newton-Raphson method and the definition of the chemically allowed interval. This combined algorithm is very impressive in terms of reliability, robustness, and speed.