The Numerov process over a non-uniform grid

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