Abstract
The solution of a bifurcation problem is often obtained by replacing the original equation by an extended problem. An asymptotic expansion is derived for the discretization error of the approximate solution of the extended system.
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References
K. Atkinson, A survey of numerical methods for the solution of Fredholm integral equations of the second kind. SIAM, Philadelphia, (1976).
R. Caluwaerts, An asymptotic expansion for the discretization error of a geometrically isolated solution of a non-linear equation. In preparation.
R. Caluwaerts, The use of a Singular extended system for the numerical computation of bifurcation points. In preparation.
R. Caluwaerts, A direct method for the determination of non-simple turning points. In preparation.
H.B. Keller, Geometrically isolated non-isolated solutions and their approximation. SIAM J. Numer. Anal. v. 18, 822–838 (1982).
G. Moore, The numerical treatment of non-trivial bifurcation points. Numer. Funct. Anal, and Optimiz., v. 2, 441–472 (1980).
G. Moore and A. Spence, The calculation of turning points of non-linear equations. SIAM J. Numer. Anal., v. 17, 567–576, (1980).
D. Roose and R. Caluwaerts, Direct methods for the computation of non-simple turning points corresponding to a cusp. These proceedings.
D. Roose and R. Piessens, Numerical computation of nonsimple turning points and cusps. Report TW 60, Dept. of Computer Science, Universiteit Leuven (1983) ( Submitted to Numer. Math.).
R. Seydel, Numerical computation of branch points in ordinary differential equations, Numer. Math,, v. 32, 51–68, (1979).
H. Stetter, Asymptotic expansions for the error of discretization algorithms for non-linear functional equations. Numer. Math., v. 7, 18–31, (1965).
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© 1984 Springer Basel AG
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Caluwaerts, R. (1984). The Use of Extrapolation for the solution of Bifurcation Problems. In: Küpper, T., Mittelmann, H.D., Weber, H. (eds) Numerical Methods for Bifurcation Problems. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 70. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6256-1_7
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DOI: https://doi.org/10.1007/978-3-0348-6256-1_7
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-6257-8
Online ISBN: 978-3-0348-6256-1
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