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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
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.
- [1]
L.
Fox, The numerical solution of two-point boundary problems in
ordinary differential equations, Oxford University Press, New York,
1957. MR
0102178 (21 #972)
- [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
(40 #6776)
- [3]
Victor
Pereyra, Iterated deferred corrections for nonlinear operator
equations, Numer. Math. 10 (1967), 316–323. MR 0221760
(36 #4812)
- [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
(30 #5505)
- [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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DOI:
http://dx.doi.org/10.1090/S0025-5718-1972-0373296-3
PII:
S 0025-5718(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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