Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 

 

Difference approximations for boundary and eigenvalue problems for ordinary differential equations


Author: Heinz-Otto Kreiss
Journal: Math. Comp. 26 (1972), 605-624
MSC: Primary 65L10
MathSciNet review: 0373296
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Abstract: The boundary value problem for ordinary differential equations is considered and a general theory for difference approximation is developed. In particular, the influence of extra boundary conditions is investigated and the eigenvalue problem is considered in detail.


References [Enhancements On Off] (What's this?)

  • [1] L. Fox, The numerical solution of two-point boundary problems in ordinary differential equations, Oxford University Press, New York, 1957. MR 0102178
  • [2] Herbert B. Keller, Accurate difference methods for linear ordinary differential systems subject to linear constraints, SIAM J. Numer. Anal. 6 (1969), 8–30. MR 0253562
  • [3] Victor Pereyra, Iterated deferred corrections for nonlinear operator equations, Numer. Math. 10 (1967), 316–323. MR 0221760
  • [4] Hans J. Stetter, Asymptotic expansions for the error of discretization algorithms for non-linear functional equations, Numer. Math. 7 (1965), 18–31. MR 0175320

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1972-0373296-3
Keywords: Ordinary differential equation, boundary value problem, eigenvalue problem, difference approximation
Article copyright: © Copyright 1972 American Mathematical Society