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Asymptotic error expansions and discrete newton methods for elliptic boundary value problems

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Numerical Integration of Differential Equations and Large Linear Systems

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 968))

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References

  1. Allgower,E.,K.Böhmer, S.Mc Cormick: Discrete correction methods for operator equations, in "Numerical solution of nonlinear equations",Eds.:E.Allgower, K.Glashoff, H.-O.Peitgen, 30–97 (1981).

    Google Scholar 

  2. Ames, W.F.: Nonlinear partial differential equations in engineering, Academic Press, New York-London (1965).

    MATH  Google Scholar 

  3. Böhmer, K.: Discrete Newton methods and iterated defect corrections, Numer.Math.37, 167–192(1981).

    Article  MathSciNet  MATH  Google Scholar 

  4. Böhmer, K.: Asymptotic expansions for the discretization error in Poisson's equation on general domains, in "Multivariate Approximation Theory",Eds.W.Schempp, K.Zeller, ISNM 51,30–45 (1979).

    MATH  Google Scholar 

  5. Böhmer,K.: High order difference methods for quasilinear elliptic boundary value problems on general regions, Math.Research Center, University of Wisconsin-Madison, Technical Summary Report Nr. 2042, 1980.

    Google Scholar 

  6. Böhmer, K.: Asymptotic expansion for the discretization error in linear elliptic boundary value problems on general regions, Math.Z. 177, 235–255 (1981).

    Article  MathSciNet  MATH  Google Scholar 

  7. Collatz, L.: Bemerkungen zur Fehlerabschätzung für das Differenzenverfahren bei partiellen Differentialgleichungen, Z. Angew. Math. Mech. 13, 56–57 (1933).

    Article  MATH  Google Scholar 

  8. Frank, R.: The method of iterated defect-correction and its application to two-point boundary value problems, Part I./II, Numer. Math. 25, 409–419 (1976), 27 407–420 (1977).

    Article  MathSciNet  MATH  Google Scholar 

  9. Frank, R., J. Hertling, C.W. Ueberhuber: A new approach to iterated defect corrections.

    Google Scholar 

  10. Gerschgorin, S.: Fehlerabschätzung für das Differenzenverfahren zur Lösung partieller Differentialgleichungen, Z. Angew. Math. Mech. 10, 373–382 (1930).

    Article  MATH  Google Scholar 

  11. Mikelads, S.: Neue Methoden der Integration von elliptischen und parabolischen Differentialgleichungen, Izv. Akad. Nauk SSSR, Seria Mat. 5, 57–74 (1941) (russian).

    Google Scholar 

  12. Pereyra, V.: Iterated deferred corrections for nonlinear operator equations, Numer. Math., 10, 316–323 (1967).

    Article  MathSciNet  MATH  Google Scholar 

  13. Pereyra, V.: Highly accurate numerical solution of casilinear elliptic boundary value problems in n dimensions, Math. Comp., 24, 771–783 (1970).

    MathSciNet  MATH  Google Scholar 

  14. Pereyra, V., W. Proskurowski and O. Widlund: High order fast Laplace solvers for the Dirichlet problem on general regions, Math. Comp., 31, 1–16 (1977).

    Article  MathSciNet  MATH  Google Scholar 

  15. Shortley, G., R. Weller: The numerical solution of Laclace's equation, J. Appl. Phys. 9, 334–348 (1938).

    Article  MATH  Google Scholar 

  16. Wasow, W.: Discrete approximations to elliptic differential equations, Z. Angew. Math. Phys. 6, 81–97 (1955).

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Fachbereich Mathematik der Universität Marburg Lahnberge, D-3550, Marburg

    Klaus Böhmer

Authors
  1. Klaus Böhmer
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Juergen Hinze

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© 1982 Springer-Verlag

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Böhmer, K. (1982). Asymptotic error expansions and discrete newton methods for elliptic boundary value problems. In: Hinze, J. (eds) Numerical Integration of Differential Equations and Large Linear Systems. Lecture Notes in Mathematics, vol 968. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0064896

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  • DOI: https://doi.org/10.1007/BFb0064896

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11970-8

  • Online ISBN: 978-3-540-39374-0

  • eBook Packages: Springer Book Archive

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