Affine-invariant monotone iteration methods with application to systems of nonlinear two-point boundary value problems
Voller, Rudolf L.
Applications of Mathematics, Tome 37 (1992), p. 123-138 / Harvested from Czech Digital Mathematics Library
Access to full text
Full (PDF)

In this paper we present a new theorem for monotone including iteration methods. The conditions for the operators considered are affine-invariant and no topological properties neither of the linear spaces nor of the operators are used. Furthermore, no inverse-isotony is demanded. As examples we treat some systems of nonlinear ordinary differential equations with two-point boundary conditions.

Publié le : 1992-01-01
Classification:  34B15,  47H07,  65J15,  65L10 
@article{104496,
     author = {Rudolf L. Voller},
     title = {Affine-invariant monotone iteration methods with application to systems of nonlinear two-point boundary value problems},
     journal = {Applications of Mathematics},
     volume = {37},
     year = {1992},
     pages = {123-138},
     zbl = {0754.65057},
     mrnumber = {1149162},
     language = {en},
     url = {http://dml.mathdoc.fr/item/104496}
}

Voller, Rudolf L. Affine-invariant monotone iteration methods with application to systems of nonlinear two-point boundary value problems. Applications of Mathematics, Tome 37 (1992) pp. 123-138. http://gdmltest.u-ga.fr/item/104496/

Alefeld G. Monotone Regula-falsi-ähnliche Verfahren bei nichtkonvexen Operatorgleichungen, Beitr. Numer. Math. 8 (1980), 15-30. (1980) | MR 0564583 | Zbl 0425.65034

Frommer N. Monotonicity of Brown's Method, Z. Angew. Math. Mech. 68 (1988), 101-110. (1988) | Article | MR 0931771 | Zbl 0663.65047

Korrnan P.; Leung A. W. A general monotone scheme for elliptic systems with applications to ecological models, Proc. Roy. Soc. Edinb. 102A (1986), 315-325. (1986)

Krasnoselski M. Positive Solutions of Operator Equations, Noordhoff, Groningen, 1964. (1964) | MR 0181881

Mckenna P. J.; Walter W. On the Dirichlet Problem for Elliptic Systems, Appl. Anal. 21 (1986), 207-224. (1986) | Article | MR 0840313 | Zbl 0593.35042

Ortega J. M.; Rheinboldt W.C. Iterative Solutions of Nonlinear Equations in Several Variables, Acad. Press, New York, 1970. (1970) | MR 0273810

Potra F. A. Newton-like methods with monotone convergence for solving nonlinear operator equations, Nonl. Anal. Th., Meth. Appl. 11 (1987), 697-717. (1987) | MR 0893775 | Zbl 0633.65050

Potra F. A. Monotone iterative methods for nonlinear operator equations, Numer. Funct. Anal. and Optimiz. 9 (1987), 809-843. (1987) | MR 0910856 | Zbl 0636.65056

Potra F.A.; Rheinboldt W.C. On the monotone convergence of Newton's method, Computing 36 (1986), 81-90. (1986) | Article | MR 0832932 | Zbl 0572.65034

Schmidt J. W.; Schneider H. Monoton einschließende Verfahren bei additiv zerlegbaren Gleichungen, Z. Angew. Math. Mech. 63 (1983), 3-11. (1983) | MR 0701830 | Zbl 0519.65036

Schmidt J. W.; Schneider H. Enclosing methods in perturbated nonlinear operator equations, Comput. 32 (1984), 1-11. (1984) | MR 0736257

Voller R. L. Monoton einschließende Newton-ähnliche Iterationsverfahren in halbgeordneten Räumen mit nicht notwendig regularem Kegel, Dissertation, Düsseldorf 1982. (1982)

Voller R. L. Iterative Einschließung von Lösungen nichtlinearer Differentialgleichungen durch Newton-ähnliche Iterationsverfahren, Apl. Mat. 31 (1986), 1-18. (1986) | MR 0836798

Voss H. Ein neues Verfahren zur Einschließung der Lösungen von Operatorgleichungen, Z. Angew. Math. Mech. 56 (1976), 218-219. (1976) | Article | MR 0408240 | Zbl 0341.65040