# On numerical solution of multiparameter Sturm-Liouville spectral problems

Banach Center Publications (1994)

- Volume: 29, Issue: 1, page 275-281
- ISSN: 0137-6934

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topLevitina, T.. "On numerical solution of multiparameter Sturm-Liouville spectral problems." Banach Center Publications 29.1 (1994): 275-281. <http://eudml.org/doc/262571>.

@article{Levitina1994,

abstract = {The method proposed here has been devised for solution of the spectral problem for the Lamé wave equation (see [2]), but extended lately to more general problems. This method is based on the phase function concept or the Prüfer angle determined by the Prüfer transformation cotθ(x) = y'(x)/y(x), where y(x) is a solution of a second order self-adjoint o.d.e. The Prüfer angle θ(x) has some useful properties very often being referred to in theoretical research concerning both single- and multi-parameter Sturm-Liouville spectral problems (see e.g. [6,14,5]). All these properties may be useful for numerical solution of the above problems as well. For an account of numerical methods for solving the single-parameter Sturm-Liouville spectral problem by means of a modified Prüfer transformation one is referred to [1,11,9].},

author = {Levitina, T.},

journal = {Banach Center Publications},

keywords = {Lamé wave equation; Prüfer transformation; multi-parameter Sturm-Liouville spectral problems},

language = {eng},

number = {1},

pages = {275-281},

title = {On numerical solution of multiparameter Sturm-Liouville spectral problems},

url = {http://eudml.org/doc/262571},

volume = {29},

year = {1994},

}

TY - JOUR

AU - Levitina, T.

TI - On numerical solution of multiparameter Sturm-Liouville spectral problems

JO - Banach Center Publications

PY - 1994

VL - 29

IS - 1

SP - 275

EP - 281

AB - The method proposed here has been devised for solution of the spectral problem for the Lamé wave equation (see [2]), but extended lately to more general problems. This method is based on the phase function concept or the Prüfer angle determined by the Prüfer transformation cotθ(x) = y'(x)/y(x), where y(x) is a solution of a second order self-adjoint o.d.e. The Prüfer angle θ(x) has some useful properties very often being referred to in theoretical research concerning both single- and multi-parameter Sturm-Liouville spectral problems (see e.g. [6,14,5]). All these properties may be useful for numerical solution of the above problems as well. For an account of numerical methods for solving the single-parameter Sturm-Liouville spectral problem by means of a modified Prüfer transformation one is referred to [1,11,9].

LA - eng

KW - Lamé wave equation; Prüfer transformation; multi-parameter Sturm-Liouville spectral problems

UR - http://eudml.org/doc/262571

ER -

## References

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- [6] E. A. Coddington and N. Levinson, Theory of Ordinary Differential Equations, McGraw-Hill, New York 1955. Zbl0064.33002
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- [8] M. V. Fedoryuk, Diffraction of waves by a tri-axial ellipsoid, Differentsial'nye Uravneniya 25 (11) (1989), 1990-1995 (in Russian). Zbl0699.35052
- [9] D. I. Kitoroagè, N. V. Konyukhova and B. S. Pariĭskiĭ, A Modified Phase Function Method for Problems Concerning Bound States of Particles, Soobshch. Prikl. Mat., Vychisl. Tsentr Akad. Nauk SSSR, Moscow 1986 (in Russian).
- [10] T. V. Levitina, Conditions of applicability of an algorithm for solution of two-parameter self-adjoint boundary value problems, Zh. Vychisl. Mat. i Mat. Fiz. 31 (5) (1991), 689-697 (in Russian); English transl.: USSR Comput. Math. and Math. Phys. 31 (1991). Zbl0751.65054
- [11] T. V. Pak, A study of some singular problems with parameters for systems of ordinary differential equations and computation of spheroidal wave functions, thesis, Vychisl. Tsentr Akad. Nauk SSSR, 1986 (in Russian).
- [12] R. G. D. Richardson, Theorems of oscillation for two linear differential equations of the second order with two parameters, Trans. Amer. Math. Soc. 13 (1912), 22-34. Zbl43.0400.03
- [13] B. D. Sleeman, Singular linear differential operators with many parameters, Proc. Roy. Soc. Edinburgh. Sect. A 71 (1973), 199-232. Zbl0323.34017
- [14] L. Turyn, Sturm-Liouville problems with several parameters, J. Differential Equations 38 (3) (1980), 239-259. Zbl0421.34023

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