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Deferred correction for the integral equation eigenvalue problem

Published online by Cambridge University Press:  17 February 2009

K. W. Chu  and
A. Spence
A. Spence
Affiliation:
School of Mathematics, University of Bath, Claverton Down, Bath BA2 7AY, United Kingdom
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Abstract

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This paper considers the improvement of approximate eigenvalues and eigenfunctions of integral equations using the method of deferred correction. A convergence theorem is proved and a numerical example illustrating the theory is given.

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 22 , Issue 4 , April 1981 , pp. 474 - 487
Copyright
Copyright © Australian Mathematical Society 1981

References

[1]Anselone, P. M. and Rall, L. B., “The solution of characteristic value-vector problems by Newton's method”, Number. Math. 11 (1968), 38–45.CrossRefGoogle Scholar
[2]Atkinson, K. E., “Convergence rates for approximate eigenvalues of compact integral operators”, SIAM J. Numer. Anal. 12 (1975), 213–221.CrossRefGoogle Scholar
[3]Atkinson, K. E., A survey of numerical method for the solution of Fredholm integral equations of the second kind, Society for Industrial and Applied Mathematics, (1976).Google Scholar
[4]Baker, C. T. H., “The deferred approach to the limit for eigenvalues of integral equations by iterations”, SIAM J. Numer. Anal. 15 (1978), 1112–1124.Google Scholar
[5]Baker, C. T. H., The numerical treatment of integral equation, Clarendon Press, (1977).Google Scholar
[6]Chatelin, F. E., “Numerical computation of the eigenelements of linear integral equations by iterations”, SIAM J. Numer. Anal. 15 (1978), 1112–1124.CrossRefGoogle Scholar
[7]Chu, K. W., The improvement of approxiamte solutions of the integral equation eigenvalue problem (Ph. D. Thesis, University of Bath, 1980).Google Scholar
[8]Fox, L. and Goodwin, E. T., “The numerical solution of nonsingular linear integral equations”, Phil. Trans. Roy. Soc. A, 245, (1953), 501–534.Google Scholar
[9]Hackbush, W., “On the computation of approximate eigenvalues and eigenfunctions of elliptic operators by means of a multigrid method”, SIAM J. Numer. Anal. 16, (1979), 201–215.CrossRefGoogle Scholar
[10]Mayers, D. F., “Fredholm equations of first and third kinds”, Chapters 11, 12 of Numerical solution of ordinary and partial differential equations (ed. Fox, L.) (Pergamon Press, 1962).Google Scholar
[11]Pereyar, V., “On omproving an approximate solution of a functional equation by deferred corrections”, Numer. Math. 8 (1966), 376–391.CrossRefGoogle Scholar
[12]Spence, A., “On the convergence of the Nyström method for the integral equation eigenvalue problem”, Numer. Math. 25 (1975), 57–66.CrossRefGoogle Scholar
[13]Spence, A., “Error Bounds and Estimates for Eigenvalues of Integral Equations II”, Numer. Math. 32 (1979), 139–146.CrossRefGoogle Scholar
[14]Stetter, H. J., “The defect correction principle and discretization methods”, Numer. Math. 29 (1978), 425–443.CrossRefGoogle Scholar
[15]Stewart, G. W., “Error and Perturbation bounds for subspaces associated with certain eigenvalue problems”, SIAM Rev. 15 (1973), 727–764.CrossRefGoogle Scholar
[16]Watt, J. M., “Convergence and stability of discretization methods for functional equations”, Computer J. 11 (1968), 77–82.CrossRefGoogle Scholar
[17]Wilkinson, J. H., The algebraic eigenvalue problem, (Oxford University Press, 1965).Google Scholar