Palusinski O A, Su Y, Fife P C
Department of Electrical and Computer Engineering, University of Arizona, Tucson 85721.
Electrophoresis. 1990 Nov;11(11):903-7. doi: 10.1002/elps.1150111104.
This paper presents a new numerical method for computation of solutions of prototypical equations of isotachophoresis. Numerical computation is complicated because the Poisson equation, which relates electrostatic potential to space charge density, contains a small parameter. This parameter is usually assumed to have the value of zero. Under this assumption the Poisson differential equation is replaced by an algebraic equation, which is often called the equation of electroneutrality, because it indeed states that the electrolyte is electrically neutral this assumption were not studied in the past. Here we propose an iterative procedure which allows for computation of solutions without the assumption of electroneutrality. The accuracy is controlled by a number of iterations and is limited by a computer round-off error only. The method is based on our previously published theory of existence and uniqueness of solutions of isotachophoretic equations. Details of the computational algorithm for prototypical equations of isotachophoresis are given. A numerical example and comparison with previously published data are also provided.
本文提出了一种用于计算等速电泳典型方程解的新数值方法。数值计算很复杂，因为将静电势与空间电荷密度联系起来的泊松方程包含一个小参数。该参数通常假定为零值。在此假设下，泊松微分方程被一个代数方程所取代，该代数方程常被称为电中性方程，因为它确实表明电解质是电中性的，而过去并未研究过此假设。在此我们提出一种迭代程序，该程序允许在不假设电中性的情况下计算解。精度由迭代次数控制，并且仅受计算机舍入误差限制。该方法基于我们先前发表的等速电泳方程解的存在性和唯一性理论。给出了等速电泳典型方程计算算法的详细信息。还提供了一个数值示例以及与先前发表数据的比较。
