On numerical solution of multiparameter Sturm-Liouville spectral problems

T. Levitina

Banach Center Publications (1994)

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

Abstract

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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].

How to cite

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Levitina, 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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