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On the solution of the equations arising from collocation with cubic $ B$-splines


Author: Richard F. Sincovec
Journal: Math. Comp. 26 (1972), 893-895
MSC: Primary 65L10; Secondary 65N35
MathSciNet review: 0314231
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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 [Enhancements On Off] (What's this?)

  • [1] 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.
  • [2] 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
  • [3] 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 0309333
  • [4] R. D. Russell and L. F. Shampine, A collocation method for boundary value problems, Numer. Math. 19 (1972), 1–28. MR 0305607
  • [5] 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

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1972-0314231-3
Keywords: Boundary-value problems, collocation, spline functions
Article copyright: © Copyright 1972 American Mathematical Society