zbMATH — the first resource for mathematics

Iterative variants of the Nystrom method for the numerical solution of integral equations. (English) Zbl 0267.65089

65R20 Numerical methods for integral equations
Full Text: DOI EuDML
[1] Anselone, P. M.: Convergence and error bounds for approximate solutions of integral and operator equations. In: Error in digital computation, vol. 2, ed. by L. B. Rall, p. 231-252. New York: Wiley & Sons 1965 · Zbl 0158.34102
[2] Anselone, P. M.: Collectively compact operator approximation theory. Englewood Cliffs, New Jersey: Prentice-Hall 1971 · Zbl 0228.47001
[3] Atkinson, K. E.: The numerical solution of Fredholm in tegral equations of the second kind. SIAM J. Numer. Anal.4, 337-348 (1967) · Zbl 0155.47404
[4] Atkinson, K. E.: Iterative Methods for the numerical solution of Fredholm integral equations of the second kind. Technical Report, Computer Center, Australian Natl. Univ., Canberra · Zbl 0353.65069
[5] Atkinson, K. E.: A survey of numerical methods for the solution of Fredholm integral equations of the second kind, to appear in the proceedings of the symposium ?Numerical Solution of the Integral Equations with Physical Applications?, 1971 Fall Meeting of SIAM, ed., Ben Noble
[6] Atkinson, K. E.: The numerical evaluation of fixed points for completely continuous operators. SIAM J. Numer. Anal.,10, 799-807 (1973) · Zbl 0266.65041
[7] Atkinson, K. E.: Bifurcating solutions for approximate problems. Submitted for publication
[8] Brakhage, H.: Über die numerische Behandlung von Integralgleichungen nach der Quadraturformelmethode. Numer. Math.2, 183-196 (1960) · Zbl 0142.11903
[9] Bückner, H.: A special method of successive approximations for Fredholm integral equations. Duke Math. J.15, 197-206 (1948) · Zbl 0030.39201
[10] Hoog, F. de, Weiss, R.: Asymptotic expansions for product integration. Math. Comp.,27, 295-306 (1973) · Zbl 0303.65023
[11] Fox, L., Goodwin, E. T.: The numerical solution of non-singular linear integral equations. Philos. Trans. Roy. Soc. London A245, 501-534 (1953) · Zbl 0050.12902
[12] Garabedian, P. R.: Partial differential equations. New York: Wiley & Sons 1964 · Zbl 0124.30501
[13] Hashimoto, M.: A method of solving large matrix equations reduced from Fredholm integral equations of the second kind. J. Assoc. Comput. Mach.17, 629-636 (1970) · Zbl 0211.46704
[14] Kantorovich, L. V., Akilov, G. P.: Functional analysis in normed spaces. London: Pergamon Press 1964 · Zbl 0127.06104
[15] Kantorovich, L. V., Krylov, V. I.: Approximate methods of higher analysis. Groningen, Netherlands: P. Noordhoff, Ltd. 1964 · Zbl 0083.35301
[16] Krasnoselskii, M. A.: Topological methods in the theory of nonlinear integral equations. London: Pergamon Press 1964
[17] Milne-Thomson, L. M.: Theoretical hydrodynamics, 5th ed. MacMillan 1968 · Zbl 0164.55802
[18] Moore, R. H.: Newton’s method and variations. In: Nonlinear integral equations, ed. by P. M. Anselone. Madison, Wisconsin: Univ. of Wisconsin Press 1964 · Zbl 0123.31803
[19] Moore, R. H.: Approximations to nonlinear operator equations and Newton’s method. Numer. Math.12, 23-34 (1968) · Zbl 0165.17301
[20] Nyström, E. J.: Über die praktische Auflösung von Integralgleichungen mit Anwendungen auf Randwertaufgaben. Acta Math.54, 185-204 (1930) · JFM 56.0342.01
[21] Petryshyn, W. V.: On a general iterative method for the approximate solution of linear operator equations. Math. Comp.17, 1-10 (1963) · Zbl 0111.31701
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.