A comparison of some numerical methods for twopoint boundary value problems
Author:
James M. Varah
Journal:
Math. Comp. 28 (1974), 743755
MSC:
Primary 65L10
MathSciNet review:
0373300
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Abstract: In this paper we discuss and compare two useful variable mesh schemes for linear secondorder twopoint boundary value problems: the midpoint rule and collocation with cubic Hermite functions. We analyze the stability of the blocktridiagonal factorization for solving the linear systems, compare the amount of computer time required, and test the methods on some particular numerical problems.
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 [1]
 G. F. Carrier, "Singular perturbation theory and geophysics," SIAM Rev., v. 12, 1970, pp. 175193.
 [2]
 G. de Boor & B. Swartz, "Collocation at Gaussian points," SIAM J. Numer. Anal., v. 10, 1973, pp. 582606. MR 0373328 (51:9528)
 [3]
 W. B. Gragg, "On extrapolation algorithms for ordinary initial value problems," J. Soc. Indust. Appl. Math. Ser. B Numer. Anal., v. 2, 1965, pp. 384403. MR 34 #2191. MR 0202318 (34:2191)
 [4]
 H. B. Keller, "Accurate difference methods for linear ordinary differential systems subject to linear constraints," SIAM J. Numer. Anal., v. 6, 1969, pp. 830. MR 40 #6776. MR 0253562 (40:6776)
 [5]
 R. D. Russell, "Collocation for systems of boundary value problems," SIAM J. Numer. Anal. (Submitted.)
 [6]
 R. D. Russell & L. F. Shampine, "A collocation method for boundary value problems," Numer. Math., v. 19, 1972, pp. 128. MR 46 #4737. MR 0305607 (46:4737)
 [7]
 R. D. Russell & J. M. Varah, "Equivalences in global methods for twopoint boundary value problems," (In preparation.)
 [8]
 M. H. Schultz, Spline Analysis, PrenticeHall, Englewood Cliffs, N.J., 1973. MR 0362832 (50:15270)
 [9]
 J. M. Varah, "On the solution of blocktridiagonal systems arising from certain finitedifference equations," Math. Comp., v. 26, 1972, pp. 859868. MR 0323087 (48:1445)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718197403733004
PII:
S 00255718(1974)03733004
Keywords:
Twopoint boundary value problems,
collocation,
Galerkin method,
finitedifferences,
operation counts,
numerical stability
Article copyright:
© Copyright 1974 American Mathematical Society
