Efficient Computation of Higher Sturm-Liouville Eigenvalues

作者: Alan L. Andrew

DOI: 10.1007/978-3-0348-6303-2_1

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摘要: A survey is given of recent work directed towards efficient and accurate computation higher eigenvalues Sturm-Liouville problems. Particular emphasis to Paine, de Hoog, Anderssen the author on a simple asymptotic correction technique which, at negligible extra cost, dramatically improves accuracy finite difference element estimates generally also for lower eigenvalues. Some new numerical results are presented which illustrate viability combining with extrapolation, several suggestions made future research.

参考文章(19)
J. W. Paine, F. R. de Hoog, R. S. Anderssen, On the correction of finite difference eigenvalue approximations for Sturm-Liouville problems Computing. ,vol. 26, pp. 123- 139 ,(1981) , 10.1007/BF02241779
G Doherty, MJ Hamilton, PG Burton, EI von Nagy-Felsobuki, A numerical variational method for calculating accurate vibrational energy separations of small molecules and their ions Australian Journal of Physics. ,vol. 39, pp. 749- 760 ,(1986) , 10.1071/PH860749
John Paine, Frank de Hoog, Uniform estimation of the eigenvalues of Sturm–Liouville problems The Journal of The Australian Mathematical Society. Series B. Applied Mathematics. ,vol. 21, pp. 365- 383 ,(1980) , 10.1017/S0334270000002459
Alan L. Andrew, Correction of finite difference eigenvalues of periodic Sturm-Liouville problems The Journal of The Australian Mathematical Society. Series B. Applied Mathematics. ,vol. 30, pp. 460- 469 ,(1989) , 10.1017/S0334270000006391
John Paine, A Numerical Method for the Inverse Sturm–Liouville Problem SIAM Journal on Scientific and Statistical Computing. ,vol. 5, pp. 149- 156 ,(1984) , 10.1137/0905011
John W Paine, Alan L Andrew, Bounds and higher-order estimates for Sturm-Liouville eigenvalues Journal of Mathematical Analysis and Applications. ,vol. 96, pp. 388- 394 ,(1983) , 10.1016/0022-247X(83)90048-3
Alan L. Andrew, John W. Paine, Correction of Numerov's eigenvalue estimates Numerische Mathematik. ,vol. 47, pp. 289- 300 ,(1985) , 10.1007/BF01389712
J. D. PRYCE, Error Control of Phase-Function Shooting Methods for Sturm-Liouville Problems Ima Journal of Numerical Analysis. ,vol. 6, pp. 103- 123 ,(1986) , 10.1093/IMANUM/6.1.103