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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
DOI: https://doi.org/10.1090/S0025-5718-1972-0373296-3
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 Univ. Press, Oxford, 1957. MR 21 #972. MR 0102178 (21:972)
  • [2] H. B. Keller, ``Accurate difference methods for linear ordinary differential systems subject to linear constraints,'' SIAM J. Numer. Anal., v. 6, 1969, pp. 8-30. MR 40 #6776. MR 0253562 (40:6776)
  • [3] V. Pereyra, ``Iterated deferred corrections for nonlinear operator equations,'' Numer. Math., v. 10, 1967, pp. 316-323. MR 36 #4812. MR 0221760 (36:4812)
  • [4] H. J. Stetter, ``Asymptotic expansions for the error of discretization algorithms for non-linear functional equations,'' Numer. Math., v. 7, 1965, pp. 18-31. MR 30 #5505. MR 0175320 (30:5505)

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Additional Information

DOI: https://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

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