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Automatic solution of Sturm-Liouville problems using the Pruess method. (English) Zbl 0747.65070

Basing on the well known reliable code SLEIGN for solution of Sturm- Liouville problems, the authors propose now a new code for automatic solution for the problem based on a numerical method different from that used by SLEIGN. Namely, an essential feature of the method is the approximation of the coefficient functions of the differential equation and some eigenvalues estimates given by S. Pruess [SIAM J. Numer. Anal. 10, 55-68 (1973; Zbl 0224.65025)].
Because of automatic meshing and a very simple algorithm for interval truncation, the new code is applicable to both regular and singular Sturm-Liouville problems; the numerical experiments presented in the paper show that there are a significant number of problems on which the authors’ code (modification SLO2F) runs faster than SLEIGN.
Reviewer: O.Titow (Berlin)

MSC:

65L15 Numerical solution of eigenvalue problems involving ordinary differential equations
65L50 Mesh generation, refinement, and adaptive methods for ordinary differential equations
34L15 Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators

Citations:

Zbl 0224.65025

Software:

SLEDGE; NAG; d02kef
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Full Text: DOI

References:

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