Abstract
Some iterative variants of the Nyström method for the numerical solution of linear and nonlinear integral equations are introduced and discussed. Numerical examples are given; some are for integral equations with singular kernel functions.
Similar content being viewed by others
Bibliography
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
Anselone, P. M.: Collectively compact operator approximation theory. Englewood Cliffs, New Jersey: Prentice-Hall 1971
Atkinson, K. E.: The numerical solution of Fredholm in tegral equations of the second kind. SIAM J. Numer. Anal.4, 337–348 (1967)
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
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
Atkinson, K. E.: The numerical evaluation of fixed points for completely continuous operators. SIAM J. Numer. Anal.,10, 799–807 (1973)
Atkinson, K. E.: Bifurcating solutions for approximate problems. Submitted for publication
Brakhage, H.: Über die numerische Behandlung von Integralgleichungen nach der Quadraturformelmethode. Numer. Math.2, 183–196 (1960)
Bückner, H.: A special method of successive approximations for Fredholm integral equations. Duke Math. J.15, 197–206 (1948)
Hoog, F. de, Weiss, R.: Asymptotic expansions for product integration. Math. Comp.,27, 295–306 (1973)
Fox, L., Goodwin, E. T.: The numerical solution of non-singular linear integral equations. Philos. Trans. Roy. Soc. London A245, 501–534 (1953)
Garabedian, P. R.: Partial differential equations. New York: Wiley & Sons 1964
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)
Kantorovich, L. V., Akilov, G. P.: Functional analysis in normed spaces. London: Pergamon Press 1964
Kantorovich, L. V., Krylov, V. I.: Approximate methods of higher analysis. Groningen, Netherlands: P. Noordhoff, Ltd. 1964
Krasnoselskii, M. A.: Topological methods in the theory of nonlinear integral equations. London: Pergamon Press 1964
Milne-Thomson, L. M.: Theoretical hydrodynamics, 5th ed. MacMillan 1968
Moore, R. H.: Newton's method and variations. In: Nonlinear integral equations, ed. by P. M. Anselone. Madison, Wisconsin: Univ. of Wisconsin Press 1964
Moore, R. H.: Approximations to nonlinear operator equations and Newton's method. Numer. Math.12, 23–34 (1968)
Nyström, E. J.: Über die praktische Auflösung von Integralgleichungen mit Anwendungen auf Randwertaufgaben. Acta Math.54, 185–204 (1930)
Petryshyn, W. V.: On a general iterative method for the approximate solution of linear operator equations. Math. Comp.17, 1–10 (1963)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Atkinson, K. Iterative variants of the Nyström method for the numerical solution of integral equations. Numer. Math. 22, 17–31 (1974). https://doi.org/10.1007/BF01436618
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01436618