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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
DOI: https://doi.org/10.1090/S0025-5718-1972-0314231-3
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] H. B. Keller, Numerical Methods for Two-Point Boundary-value Problems, Blaisdell, Waltham, Mass., 1968. MR 37 #6038. MR 0230476 (37:6038)
  • [3] T. R. Lucas & G. W. Reddien, JR., ``Some collocation methods for nonlinear boundary value problems,'' SIAM J. Numer. Anal., v. 9, 1972, pp. 341-356. MR 0309333 (46:8443)
  • [4] R. D. Russell & L. F. Shampine, ``A collocation method for boundary value problems,'' Numer. Math., v. 19, 1972, pp. 1-28. MR 0305607 (46:4737)
  • [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 36 #6848. MR 0223801 (36:6848)

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Additional Information

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

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