Quadrature methods for integral equations of the second kind over infinite intervals
Author:
Ian H. Sloan
Journal:
Math. Comp. 36 (1981), 511523
MSC:
Primary 65R20; Secondary 45B05
MathSciNet review:
606510
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Abstract: Convergence results are proved for a class of quadrature methods for integral equations of the form . An important special case is the Nyström method, in which the integral term is approximated by an ordinary quadrature rule. For all of the methods considered here, the rate of convergence is the same, apart from a constant factor, as that of the quadrature approximation to the integral term.
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 P. M. Anselone, Collectively Compact Operator Approximation Theory and Applications to Integral Equations, PrenticeHall, Englewood Cliffs, N.J., 1971. MR 0443383 (56:1753)
 [2]
 K. E. Atkinson, "The numerical solution of integral equations on the halfline," SIAM J. Numer. Anal., v. 6, 1969, pp. 375397. MR 0253579 (40:6793)
 [3]
 C. T. H. Baker, The Numerical Treatment of Integral Equations, Clarendon Press, Oxford, 1977. MR 0467215 (57:7079)
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 C. Corduneanu, Integral Equations and Stability of Feedback Systems, Academic Press, New York, 1973. MR 0358245 (50:10710)
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 P. J. Davis & P. Rabinowitz, Methods of Numerical Integration, Academic Press, New York, 1975. MR 0448814 (56:7119)
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 E. J. Nyström, "Über die praktische Auflösung von Integralgleichungen mit Anwendungen auf Randwertaufgaben," Acta Math., v. 54, 1930, pp. 185204. MR 1555306
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 J. D. Pryce, Basic Methods of Linear Functional Analysis, Hutchinson University Library, London, 1973. MR 0358267 (50:10733)
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 I. H. Sloan, "On choosing the points in product integration," J. Math. Phys., v. 21, 1980, pp. 10321039. MR 574876 (81g:65029)
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 [12]
 J. V. Uspensky, "On the convergence of quadrature formulas related to an infinite interval," Trans. Amer. Math. Soc., v. 30, 1928, pp. 542559. MR 1501444
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198106065102
PII:
S 00255718(1981)06065102
Keywords:
Integral equation,
Fredholm equation,
equation of the second kind,
infinite interval,
Nyström method,
quadrature method
Article copyright:
© Copyright 1981
American Mathematical Society
