Advertisement

Discrete convergence of continuous mappings in metric spaces

  • Friedrich Stummel
  • Jürgen Reinhardt
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 333)

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ansorge, R.: Problemorientierte Hierarchie von Konvergenzbegriffen bei der numerischen Lösung von Anfangswertaufgaben. Math. Z. 112, 13–22 (1969).MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    — und Hass, R.: Konvergenz von Differenzenverfahren für lineare und nichtlineare Anfangswertaufgaben. Lecture Notes in Mathematics 159. Berlin-Heidelberg-New York: Springer 1970.CrossRefzbMATHGoogle Scholar
  3. 3.
    Aubin, J.P.: Approximation des espaces de distribution et des opérateurs différentiels. Bull. Soc. Math. France Mém. 12, 1–139 (1967).MathSciNetzbMATHGoogle Scholar
  4. 4.
    — Approximation of elliptic boundary-value problems. New York: Wiley 1972.zbMATHGoogle Scholar
  5. 5.
    Browder, F.E.: Approximation-solvability of nonlinear functional equations in normed linear spaces. Arch. Rat. Mech. Anal. 26, 33–42 (1967).MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Dieudonné, J.: Fundations of modern analysis. New York-London: Academic Press 1960.Google Scholar
  7. 7.
    Grigorieff, R.D.: Zur Theorie linearer approximationsregulärer Operatoren. I und II. To appear in Math. Nachr.Google Scholar
  8. 8.
    Henrici, P.: Discrete variable methods in ordinary differential equations. New York-London: Wiley 1962.zbMATHGoogle Scholar
  9. 9.
    — Error propagation for difference methods. New York-London: Wiley 1963.zbMATHGoogle Scholar
  10. 10.
    Krasnosel'skii, M.A., Vainikko, G.M., et al.: Approximate solution of operator equations. Groningen: Wolters-Noordhoff 1972.CrossRefGoogle Scholar
  11. 11.
    Lax, P.D., and Richtmyer, R.D.: Survey of the stability of linear finite difference equations. Comm. Pure Appl. Math. 9, 267–293 (1956).MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Pereyra, V.: Iterated deferred corrections for nonlinear operator equations. Numer. Math. 10, 316–323 (1967).MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Petryshyn, W.V.: Projection methods in nonlinear numerical functional analysis. J. Math. Mech. 17, 353–372 (1967).MathSciNetzbMATHGoogle Scholar
  14. 14.
    — On the approximation-solvability of nonlinear equations. Math. Ann. 177, 156–164 (1968).MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Reinhardt, J.: Diskrete Konvergenz nichtlinearer Operatoren in metrischen Räumen. Frankfurt: Diplomarbeit 1971.Google Scholar
  16. 16.
    Rinow, W.: Die innere Geometrie der metrischen Räume. Berlin-Göttingen-Heidelberg: Springer 1961.CrossRefzbMATHGoogle Scholar
  17. 17.
    Spijker, M.N.: On the structure of error estimates for finite-difference methods. Numer. Math. 18, 73–100 (1971).MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    — Equivalence theorems for non-linear finite difference methods. Numerische Lösung nichtlinearer partieller Differential-und Integrodifferentialgleichungen. Lecture Notes in Mathematics 267, 233–264. Berlin-Heidelberg-New York: Springer 1972.MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Stetter, H.J.: Stability of nonlinear discretization algorithms. In J.H. Bramble (Ed.): Numerical solution of partial differential equations, 111–123. New York: Academic Press 1966.Google Scholar
  20. 20.
    Stummel, F.: Diskrete Konvergenz linearer Operatoren. I. Math. Ann. 190, 45–92 (1970). II. Math. Z. 120, 231–264 (1971). III. To appear, Proc. Oberwolfach Conference on Linear Operators and Approximation 1971. Int. Series of Numerical Mathematics, Vol. 20. Basel: Birkhäuser.MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    — Discrete convergence of mappings. To appear, Proc. Conference on Numerical Analysis, Dublin, August 1972. New York-London: Academic Press 1973.zbMATHGoogle Scholar
  22. 22.
    — Discrete convergence of differentiable mappings. To appear.Google Scholar
  23. 23.
    Vainikko, G.M.: Galerkin's perturbation method and the general theory of approximate methods for non-linear equations. USSR Comput. Math. and Math. Phys. 7, 1–41 (1967).CrossRefGoogle Scholar
  24. 24.
    Watt, J.M.: Consistency, convergence and stability of general discretizations of the initial value problem. Numer. Math. 12, 11–22 (1968).MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1973

Authors and Affiliations

  • Friedrich Stummel
  • Jürgen Reinhardt

There are no affiliations available

Personalised recommendations