On the solution of the equations arising from collocation with cubic $B$-splines
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- by Richard F. Sincovec PDF
- Math. Comp. 26 (1972), 893-895 Request permission
Abstract:
An iterative technique for solving the equations arising from collocation with cubic $B$-splines in solving second-order nonlinear boundary-value problems is defined and shown to converge.References
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C. De Boor, The Method of Projections as Applied to the Numerical Solution of Two Point Boundary Value Problems Using Cubic Splines, Dissertation, University of Michigan, Ann Arbor, Mich., 1966.
- Herbert B. Keller, Numerical methods for two-point boundary-value problems, Blaisdell Publishing Co. [Ginn and Co.], Waltham, Mass.-Toronto, Ont.-London, 1968. MR 0230476
- Thomas R. Lucas and George W. Reddien Jr., Some collocation methods for nonlinear boundary value problems, SIAM J. Numer. Anal. 9 (1972), 341–356. MR 309333, DOI 10.1137/0709034
- R. D. Russell and L. F. Shampine, A collocation method for boundary value problems, Numer. Math. 19 (1972), 1–28. MR 305607, DOI 10.1007/BF01395926
- I. J. Schoenberg, On spline functions, Inequalities (Proc. Sympos. Wright-Patterson Air Force Base, Ohio, 1965) Academic Press, New York, 1967, pp. 255–291. MR 0223801
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Math. Comp. 26 (1972), 893-895
- MSC: Primary 65L10; Secondary 65N35
- DOI: https://doi.org/10.1090/S0025-5718-1972-0314231-3
- MathSciNet review: 0314231