Equadiff 6 pp 333-338 | Cite as

Enclosing methods for perturbed boundary value problems in nonlinear difference equations

  • J. W. Schmidt
Lectures Presented In Sections Section C Numerical Methods
Part of the Lecture Notes in Mathematics book series (LNM, volume 1192)


Finite Difference Method Nonlinear Difference Equation Linear Operator Equation Dimensional Linear Space Perturb Boundary 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    SCHMIDT, J.W., SCHNEIDER, H., Enclosina methods in perturbed nonlinear operator equations. Computing 32, 1–11 (1984).MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    COLLATZ, L., Auhaben monotoner Art, Arch. Math. (Basel) 3, 366–376 (1952).MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    NICKEL, K., The construction of a priori bounds for the solution of a two point boundary value problem with finite elements, Computing 23, 247–265 (1979).MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    SCHRÖDER, H., Operator Inequalities, New York-London: Academic Press 1980.zbMATHGoogle Scholar
  5. [5]
    SPREUER, H., A method for the computation of bounds for ordinary linear boundary value problems, J. Math. Anal. Appl. 81, 99–133 (1981).MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    WILDENAUER, P., A new method for automatical computation of error bounds for nonlinear boundary value problems, Computing 34, 131–154 (1985).MathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    ALEFELD, G., Quadratisch konvergente Einschließung von Lösungen nichtkonvexer Gleichungssysteme, Z. Angew. Math. Mech. 54, 335–345 (1974).MathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    ORTEGA, J.M., RHEINBOLDT, W.C., Monotone iterations for nonlinear equations with application to Gauss-Seidel methods, SIAM J. Numer. Anal. 4, 171–190 (1967).MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    SCHMIDT, J.W., LEONHARDT, H., Eingrenzung von Lösungen mit Hilfe der Regula falsi, Computing 6, 318–329 (1970).MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    SCHMIDT, J.W., SCHNEIDER, H., Monoton einschließende Verfahren bei additiv zerlegbaren Gleichungen, Z. Angew. Math. Mech, 63, 3–11 (1983).MathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    SCHNEIDER, N., Monotone Einschließung durch Verfahren vom Regula falsi-Typ, Computing 26, 33–44 (1981).MathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    TÖRNIG, W., Monoton konvergente Iterationsverfahren zur Lösung nichlinearer Differenzen-Randwertprobleme, Beiträge Numer. Math. 4, 245–257 (1975).zbMATHGoogle Scholar
  13. [13]
    TÖRNIG, W., Monoton einschließend konvergente Itartionsprozesse vom Gauss-Seidel-Typ, Math. Meth. Appl. Sci. 2, 489–503 (1980).CrossRefzbMATHGoogle Scholar
  14. [14]
    GROBMANN, CH., KRÄTZSCHMAR, M., Monotone Diskretisierung und adaptive Gittergenerierung fün Zwei-Punkt-Randwertaufgaben, Z. Angew Math. Mech. 65, T264–266 (1985).MathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    GROΒMANN,CH., KRÄTZSCHMAR,M., ROOS,H.-G., Uniformly enclosing discretization methods of high order for boundary value problems Math. Meth. Appl. Sci. (submitted 1985).Google Scholar

Copyright information

© Equadiff 6 and Springer-Verlag 1986

Authors and Affiliations

  • J. W. Schmidt
    • 1
  1. 1.Technical University of DresdenDresdenGermany

Personalised recommendations