Geodesic
Numerical determination of the Titchmarsh–Weyl $m$-coefficient
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 40 (2000) no. 1, pp. 112-121 Cet article a éte moissonné depuis la source Math-Net.Ru

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N. A. Gordon; J. P. Killingbeck; M. Witwit. Numerical determination of the Titchmarsh–Weyl $m$-coefficient. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 40 (2000) no. 1, pp. 112-121. http://geodesic.mathdoc.fr/item/ZVMMF_2000_40_1_a11/

[1] Weyl H., “Über gewöhnliche Differentialgleichungen mit Singujaritäten und die zugehörigen Entwicklungen willkürlicher Funktionen”, Math. Ann., 68 (1910), 220–269 | DOI | MR | Zbl

[2] Titchmarsh E. C., “On Expansions in Eigenfunctions (IV)”, Quart. J. Math., 12 (1941), 33–55 | DOI | MR

[3] Titchmarsh E. C., “On Expansions in Eigenfunctions (VII)”, Quart. Math., 16 (1945), 33–55 | MR

[4] Titchmarsh E. C., Eigenfunctions Expansions, Part I (sec. ed.), Oxford Univ. Press, 1962 | MR

[5] Brown B. M., Kirby V. G., and Pryce J. D., “A Numerical Method for the Determination of the Titchmarsh–Weyl $m$-Coefficient”, Proc Roy. Soc. London A, 435 (1991), 535–549 | DOI | MR | Zbl

[6] Brown B. M., Eastham M. S. P., Evans W. D., and Kirby V. G., “Repeated Diagonalization and the Numerical Computation of the Titchmarsh–Weyl $m(\lambda)$ Function”, Proc. Roy. Soc. London A, 445 (1994), 113–126 | DOI | MR | Zbl

[7] Kirby V. G., A Numerical Method for Determining the Titchmarsh–Weyl $m$-Coefficient and its Applications to Certain Integro-Differential Inequalities, Ph. D. thesis, Univ. Wales College of Cardiff, U.K., 1990 | Zbl

[8] Wolfram S., Mathematica, Addison-Wesley, 1988 | Zbl

[9] Konyukhova N. B. and Staroverova I. B., “Modification of the Phase Method for Singular Selfe Adjoint Sturm–Liouville Problems”, Comput. Math. Math. Phys., 37:10 (1997), 1143–1160 | MR | Zbl

[10] Kitoroage D. I., Konyukhova N. B., and Pariiskii B. S., Soobsch. Pricl. Matem., Vychisl. Tsentr AN SSSR, Moscow, 1987 (in Rus.) | MR | Zbl

[11] Konyukhova N. B., Masalovich S. E., and Staroverova I. B., “Computation of Rapidly Oscillating Eigenfunctions of a Continuous Spectrum and their Improper Integrals”, Comput. Math. Math. Phys., 35:3 (1995), 287–302 | MR | Zbl

[12] Frantz D. D., “Wrong-Way Recursion Yields More Accurate Eigenparameters for the Hydrogen-Molecule Ion”, Phys. Fev. A, 40 (1989), 1175–1184

[13] Kobeissi H., Kobeissi M., and Elhajj A., “On Computing Eigenvalues of the Schrodinger Equation for Symmetrical Potentials”, Phys. A, 22 (1989), 287–295 | DOI | MR | Zbl

[14] Killingbeck J. P., Gordon N. A., and Witwit M. R. M., “Stable Forward Shooting for Eigenvalues and Expectation Values”, Phys. Letts. A, 206 (1995), 279–282 | DOI | MR | Zbl