Approximation methods for nonlinear problems with application to two-point boundary value problems

Mathematics of Computation

Volumn 29, Issue 130, 1975, Pages 464-474

  Keller, H B ^a  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Finite difference schemes; Newtons method; Nonlinear stability; Two point boundary problems

Indexed keywords

EID: 84966247178     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-1975-0371058-7     Document Type: Article

References (12)

1. H. B. KELLER, "Accurate difference methods for linear ordinary differential systems subject to linear constraints," SIAM J. Numer. Anal., v. 6, 1969, p. 8-30.
2. H. B. KELLER, "Newton's method under mild differentiability conditions," J. Comput. System Sei., v. 4, 1970, p. 15-28.
3. H. B. KELLER, "Accurate difference methods for nonlinear two point boundary value problems," SIAM J. Numer. Anal., v. 11, 1974, p. 305-320.
4. H. B. KELLER A. B. WHITE, "Difference methods for boundary value problems in ordinary differential equations," SIAM J. Numer. Anal., v. 12, 1975. (To appear.)
5. J. M. ORTEGA W. C. RHEINBOLDT, Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, 1970.
6. R. D. RICHTMYER, Difference Methods for Initial-Value Problems, Interscience Tracts in Pure and Appl. Math., no. 4, Interscience, New York, 1957.
7. R. B. SIMPSON, "Existence and error estimates for solutions of a discrete analog of nonlinear eigen value problems," Math. Comp., v. 26, 1972, p. 359-375.
8. H. I. STETTER, "Asymptotic expansions for the error of discretization algorithms for non-linear functional equations," Numer. Math., v. 7, 1965, p. 18-31.
9. H. J. STETTER, "Stability of nonlinear discretization algorithms," Numerical Solution of Partial Differential Equations (Proc. Sympos. Univ. Maryland, 1965), Academic Press, New York, 1966, p. 111-123.
10. R. K. WEISS, "The application of implicit Runge-Kutta and collocation methods to boundary value problems," Math. Comp., v. 28, 1974, p. 449-464.
11. A. B. WHITE, Numerical Solution of Two Point Boundary Value Problems, Ph. D. Thesis, Calif. Inst. of Technology, Pasadena, 1974.
12. V. PEREYRA, "Iterated deferred corrections for nonlinear operator equations," Numer. Math., v. 10, 1967, p. 316-323.