Abstract
AbstractThe 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.
Funder
Alma Mater Studiorum - Università di Bologna
Publisher
Springer Science and Business Media LLC
Subject
Electrical and Electronic Engineering,Modeling and Simulation,Atomic and Molecular Physics, and Optics,Electronic, Optical and Magnetic Materials
Reference9 articles.
1. Numerov, B.: A new method for determining the orbits and calculating the ephemerides accounting for the perturbations. Publ. Obs. Central Astrophys. 2, 188–288 (1923). (in Russian)
2. Chow, P.C.: Computer solutions to the Schrödinger equation. Am. J. Phys. 40, 730–734 (1972)
3. Vigo-Aguiar, J., Ramos, H.: A variable-step Numerov method for the numerical solution of the Schrödinger equation. J. Math. Chem. 37(3), 255–262 (2005)
4. Press, W.H., Flannery, B.R., Teukolsky, S.A., Wetterling, W.T.: Numerical recipes: the art of scientific computing. Cambridge University Press, New York (1988)
5. Zlotnik, A.: $$\check{\rm C}$$iegis, R.: A compact higher-order finite-difference scheme for the wave equation can be strongly non-dissipative on non-uniform meshes. Appl. Math. Lett. 115, 106949 (2021)
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献