In this paper, we provide a detailed theoretical analysis of the numerical scheme introduced in J. Comput. Phys. 436 (2021) 110253 for the reaction kinetics of a class of chemical reaction networks that satisfies detailed balance condition. In contrast to conventional numerical approximations, which are typically constructed based on ordinary differential equations (ODEs) for the concentrations of all involved species, the scheme is developed using the equations of reaction trajectories, which can be viewed as a generalized gradient flow of physically relevant free energy. The unique solvability, positivity-preserving, and energy-stable properties are proved for the general case involving multiple reactions, under a mild condition on the stoichiometric matrix.

翻译：本文对J. Comput. Phys. 436 (2021) 110253中针对一类满足细致平衡条件的化学反应网络反应动力学提出的数值格式进行了详细的理论分析。与传统基于所有参与物种浓度的常微分方程(ODEs)构建的数值近似方法不同，该格式利用反应轨迹方程开发，可视为物理相关自由能的广义梯度流。在化学计量矩阵的温和条件下，证明了涉及多反应一般情形下的唯一可解性、正性保持和能量稳定性质。