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首页> 外文期刊>Computers & Chemistry >NUMERICAL STABILITY OF FINITE DIFFERENCE ALGORITHMS FOR ELECTROCHEMICAL KINETIC SIMULATIONS: MATRIX STABILITY ANALYSIS OF THE CLASSIC EXPLICIT, FULLY IMPLICIT AND CRANK-NICOLSON METHODS AND TYPICAL PROBLEMS INVOLVING MIXED BOUNDARY CONDITIONS
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NUMERICAL STABILITY OF FINITE DIFFERENCE ALGORITHMS FOR ELECTROCHEMICAL KINETIC SIMULATIONS: MATRIX STABILITY ANALYSIS OF THE CLASSIC EXPLICIT, FULLY IMPLICIT AND CRANK-NICOLSON METHODS AND TYPICAL PROBLEMS INVOLVING MIXED BOUNDARY CONDITIONS

机译：电化学动力学模拟的有限差分算法的数值稳定性：经典显式，完全隐式和Crank-NICOLSON方法的矩阵稳定性分析以及涉及混合边界条件的典型问题

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摘要

The stepwise numerical stability of the classic explicit, fully implicit and Crank-Nicolson finite difference discretizations of example diffusional initial boundary value problems from electrochemical kinetics has been investigated using the matrix method of stability analysis. Special attention has been paid to the effect of the discretization of the mixed, linear boundary condition with time-dependent coefficients on stability, assuming the two-point forward-difference approximations for the gradient at the left boundary (electrode). Under accepted assumptions one obtains the usual stability criteria for the classic explicit and fully implicit methods. The Crank-Nicolson method turns out to be only conditionally stable in contrast to the current thought regarding this method.
机译：使用稳定性分析的矩阵方法，研究了基于电化学动力学的示例扩散初始边值问题的经典显式，完全隐式和Crank-Nicolson有限差分离散化的逐步数值稳定性。假设混合线性边界条件与时间相关系数的离散化对稳定性的影响已得到特别关注，假定左边界（电极）处的梯度具有两点正向差分。在公认的假设下，可以获得经典的显式和完全隐式方法的通常稳定性标准。事实证明，与当前关于该方法的想法相比，Crank-Nicolson方法仅在条件上稳定。

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