Summary
The error in the estimate of thekth eigenvalue of a regular Sturm-Liouville problem obtained by Numerov's method with mesh lengthh isO(k 6 h 4). We show that a simple correction technique of Paine, de Hoog and Anderssen reduces the error to one ofO(k 3 h 4). Numerical examples demonstrate the usefulness of this correction even for low values ofk.
Article PDF
Avoid common mistakes on your manuscript.
References
Anderssen, R.S., de Hoog, F.R.: On the correction of finite difference eigenvalue approximations for Sturm-Liouville problems with general boundary conditions. BIT24, 401–412 (1984)
Andrew, A.L.: Numerical solution of eigenvalue problems for ordinary differential equations. In: Computational techniques and applications: CTAC-83 (J. Noye, C. Fletcher, eds.), pp. 841–852. Amsterdam: North-Holland 1984
Chawla, M.M., Katti, C.P.: On Noumerov's method for computing eigenvalues. BIT20, 107–109 (1980)
Davis, P.J., Rabinowitz, P.: Methods of numerical integration. New York: Academic Press 1975
Keller, H.B.: Numerical methods for two-point boundary value problems. Waltham, Mass.: Ginn-Blaisdell 1968
Paine, J.W.: Numerical approximation of Sturm-Liouville eigenvalues, Ph.D. Thesis, Australian National University, Canberra 1979
Paine, J.: A numerical method for the inverse Sturm-Liouville problem. SIAM J. Sci. Statist. Comput.5, 149–156 (1984)
Paine, J.W., de Hoog, F.R., Anderssen, R.S.: On the correction of finite difference eigenvalue approximations for Sturm-Liouville problems. Computing26, 123–139 (1981)
Wilkinson, J.H.: The algebraic eigenvalue problem. Oxford: University Press 1965
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Andrew, A.L., Paine, J.W. Correction of Numerov's eigenvalue estimates. Numer. Math. 47, 289–300 (1985). https://doi.org/10.1007/BF01389712
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01389712