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Numerical solution of the sturm liouville problem with periodic boundary conditions

Invited Papers

Part of the Lecture Notes in Mathematics book series (LNM,volume 228)

Abstract

A recursive algorithm for the implicit derivation of the characteristic equation of a symmetric general tridiagonal matrix of order n is derived from a finite difference discretisation of a periodic Sturm Liouville problem. The algorithm yields a Sturmian sequence of polynomials from which the eigenvalues can be obtained by the use of the well known standard bisection process. An extension to Wilkinson's method for deriving the eigenvectors of symmetric tridiagonal matrices yields the required eigenvectors of the periodic Sturm Liouville problem.

Keywords

  • Characteristic Polynomial
  • Tridiagonal Matrix
  • Inverse Iteration
  • Tridiagonal Matrice
  • Back Substitution

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© 1971 Springer-Verlag

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Evans, D.J. (1971). Numerical solution of the sturm liouville problem with periodic boundary conditions. In: Morris, J.L. (eds) Conference on Applications of Numerical Analysis. Lecture Notes in Mathematics, vol 228. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0069462

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  • DOI: https://doi.org/10.1007/BFb0069462

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-05656-0

  • Online ISBN: 978-3-540-36976-9

  • eBook Packages: Springer Book Archive