Bieniasz Lesław K
Institute of Physical Chemistry of the Polish Academy of Sciences, Department of Electrochemical Oxidation of Gaseous Fuels, ul. Zagrody 13, 30-318 Cracow, Poland.
J Comput Chem. 2004 Jun;25(8):1075-83. doi: 10.1002/jcc.20037.
The fourth-order accurate, three-point finite-difference Numerov spatial discretization provides accurate and efficient solutions to the time-dependent governing differential equations of electrochemical kinetics in one-dimensional space geometry, when the equations contain first time derivatives of the solution, second spatial derivatives, and homogeneous reaction terms only. However, the original Numerov discretization is not applicable when the governing equations involve first spatial derivative terms. To overcome this limitation, an appropriately extended Numerov discretization is required. We examine the utility of one of such extensions, first described by Chawla. Relevant discrete formulae are outlined for systems of linear governing equations involving first derivative terms, and applied to five representative example models of electrochemical transient experiments. The extended Numerov discretization proves to have an accuracy and efficiency comparable to the original Numerov scheme, and its accuracy is typically up to four orders of magnitude higher, compared to the conventional, second-order accurate spatial discretization, commonly used in electrochemistry. This results in a considerable improvement of efficiency. Therefore, the application of the extended Numerov discretization to the electrochemical kinetic simulations can be fully recommended.
当方程仅包含解的一阶时间导数、二阶空间导数和均相反应项时，四阶精度的三点有限差分努默罗夫空间离散化方法能为一维空间几何中电化学动力学的含时控制微分方程提供准确且高效的解。然而，当控制方程包含一阶空间导数项时，原始的努默罗夫离散化方法并不适用。为克服这一限制，需要一种适当扩展的努默罗夫离散化方法。我们研究了由查瓦拉首次描述的此类扩展方法之一的实用性。针对包含一阶导数项的线性控制方程组，概述了相关离散公式，并将其应用于五个具有代表性的电化学瞬态实验示例模型。扩展的努默罗夫离散化方法被证明具有与原始努默罗夫格式相当的精度和效率，并且与电化学中常用的传统二阶精度空间离散化相比，其精度通常高出多达四个数量级。这带来了效率的显著提高。因此，完全推荐将扩展的努默罗夫离散化方法应用于电化学动力学模拟。
