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Solution of Sturm-Liouville problems using modified Neumann schemes

Veerle Ledoux (UGent) and Marnix Van Daele (UGent)
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Abstract
The main purpose of this paper is to describe the extension of the successful modified integral series methods for Schrodinger problems to more general Sturm-Liouville eigenvalue problems. We present a robust and reliable modified Neumann method which can handle a wide variety of problems. This modified Neumann method is closely related to the second-order Pruess method but provides for higher-order approximations. We show that the method can be successfully implemented in a competitive automatic general-purpose software package.
Keywords
SOFTWARE, SCHRODINGER-EQUATIONS, CP METHODS, COMPUTATIONS, ERROR, SERIES, PACKAGE, Sturm-Liouville problems, eigenvalue, shooting, ORDINARY DIFFERENTIAL-EQUATIONS, PRUESS METHOD

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Citation

Please use this url to cite or link to this publication:

MLA
Ledoux, Veerle, and Marnix Van Daele. “Solution of Sturm-Liouville Problems Using Modified Neumann Schemes.” SIAM JOURNAL ON SCIENTIFIC COMPUTING 32.2 (2010): 563–584. Print.
APA
Ledoux, V., & Van Daele, M. (2010). Solution of Sturm-Liouville problems using modified Neumann schemes. SIAM JOURNAL ON SCIENTIFIC COMPUTING, 32(2), 563–584.
Chicago author-date
Ledoux, Veerle, and Marnix Van Daele. 2010. “Solution of Sturm-Liouville Problems Using Modified Neumann Schemes.” Siam Journal on Scientific Computing 32 (2): 563–584.
Chicago author-date (all authors)
Ledoux, Veerle, and Marnix Van Daele. 2010. “Solution of Sturm-Liouville Problems Using Modified Neumann Schemes.” Siam Journal on Scientific Computing 32 (2): 563–584.
Vancouver
1.
Ledoux V, Van Daele M. Solution of Sturm-Liouville problems using modified Neumann schemes. SIAM JOURNAL ON SCIENTIFIC COMPUTING. 2010;32(2):563–84.
IEEE
[1]
V. Ledoux and M. Van Daele, “Solution of Sturm-Liouville problems using modified Neumann schemes,” SIAM JOURNAL ON SCIENTIFIC COMPUTING, vol. 32, no. 2, pp. 563–584, 2010.
@article{909119,
  abstract     = {{The main purpose of this paper is to describe the extension of the successful modified integral series methods for Schrodinger problems to more general Sturm-Liouville eigenvalue problems. We present a robust and reliable modified Neumann method which can handle a wide variety of problems. This modified Neumann method is closely related to the second-order Pruess method but provides for higher-order approximations. We show that the method can be successfully implemented in a competitive automatic general-purpose software package.}},
  author       = {{Ledoux, Veerle and Van Daele, Marnix}},
  issn         = {{1064-8275}},
  journal      = {{SIAM JOURNAL ON SCIENTIFIC COMPUTING}},
  keywords     = {{SOFTWARE,SCHRODINGER-EQUATIONS,CP METHODS,COMPUTATIONS,ERROR,SERIES,PACKAGE,Sturm-Liouville problems,eigenvalue,shooting,ORDINARY DIFFERENTIAL-EQUATIONS,PRUESS METHOD}},
  language     = {{eng}},
  number       = {{2}},
  pages        = {{563--584}},
  title        = {{Solution of Sturm-Liouville problems using modified Neumann schemes}},
  url          = {{http://dx.doi.org/10.1137/090758398}},
  volume       = {{32}},
  year         = {{2010}},
}

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