The Numerov process is a solution method applicable to some classes of differential equations, that provides an error term of the fifth order in the grid size with a computational cost comparable to that of the finite-difference scheme. In the original formulation of the method, a uniform grid size is required; the paper shows a procedure for extending its applicability to a non-uniform grid in one dimension. The effectiveness of the procedure is tested on a model problem, and comparisons with other methods are carried out. Finally, it is shown how to extend the applicability of the method to a larger class of equations; among these, the mathematical model of semiconductor devices is important in view of its applications to the integrated-circuit technology.

Numerov过程是一种适用于某些类型的微分方程的求解方法，该方法提供了网格大小中的五阶误差项，并且其计算成本可与有限差分方案相比。在该方法的原始公式中，需要统一的网格大小；该文件显示了将其适用性扩展到一维非均匀网格的过程。该程序的有效性在模型问题上进行了测试，并与其他方法进行了比较。最后，显示了如何将方法的适用性扩展到更大的方程组。其中，鉴于半导体器件在集成电路技术中的应用，半导体模型的数学模型很重要。