| Title:
|
Affine-invariant monotone iteration methods with application to systems of nonlinear two-point boundary value problems (English) |
| Author:
|
Voller, Rudolf L. |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
37 |
| Issue:
|
2 |
| Year:
|
1992 |
| Pages:
|
123-138 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
partially ordered space |
| Keyword:
|
Newton-like iteration |
| Keyword:
|
affine-invariant |
| Keyword:
|
monotone including iteration methods |
| Keyword:
|
systems of nonlinear ordinary differential equations |
| MSC:
|
34B15 |
| MSC:
|
47H07 |
| MSC:
|
65J15 |
| MSC:
|
65L10 |
| idZBL:
|
Zbl 0754.65057 |
| idMR:
|
MR1149162 |
| DOI:
|
10.21136/AM.1992.104496 |
| . |
| Date available:
|
2008-05-20T18:43:16Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104496 |
| . |
| Reference:
|
[1] Alefeld G.: Monotone Regula-falsi-ähnliche Verfahren bei nichtkonvexen Operatorgleichungen.Beitr. Numer. Math. 8 (1980), 15-30. Zbl 0425.65034, MR 0564583 |
| Reference:
|
[2] Frommer N.: Monotonicity of Brown's Method.Z. Angew. Math. Mech. 68 (1988), 101-110. Zbl 0663.65047, MR 0931771, 10.1002/zamm.19880680211 |
| Reference:
|
[3] 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. |
| Reference:
|
[4] Krasnoselski M.: Positive Solutions of Operator Equations.Noordhoff, Groningen, 1964. MR 0181881 |
| Reference:
|
[5] McKenna P. J., Walter W.: On the Dirichlet Problem for Elliptic Systems.Appl. Anal. 21 (1986), 207-224. Zbl 0593.35042, MR 0840313, 10.1080/00036818608839592 |
| Reference:
|
[6] Ortega J. M., Rheinboldt W.C.: Iterative Solutions of Nonlinear Equations in Several Variables.Acad. Press, New York, 1970. MR 0273810 |
| Reference:
|
[7] Potra F. A.: Newton-like methods with monotone convergence for solving nonlinear operator equations.Nonl. Anal. Th., Meth. Appl. 11 (1987), 697-717. Zbl 0633.65050, MR 0893775, 10.1016/0362-546X(87)90037-X |
| Reference:
|
[8] Potra F. A.: Monotone iterative methods for nonlinear operator equations.Numer. Funct. Anal. and Optimiz. 9 (1987), 809-843. Zbl 0636.65056, MR 0910856, 10.1080/01630568708816262 |
| Reference:
|
[9] Potra F.A., Rheinboldt W.C.: On the monotone convergence of Newton's method.Computing 36 (1986), 81-90. Zbl 0572.65034, MR 0832932, 10.1007/BF02238194 |
| Reference:
|
[10] Schmidt J. W., Schneider H.: Monoton einschließende Verfahren bei additiv zerlegbaren Gleichungen.Z. Angew. Math. Mech. 63 (1983), 3-11. Zbl 0519.65036, MR 0701830, 10.1002/zamm.19830630103 |
| Reference:
|
[11] Schmidt J. W., Schneider H.: Enclosing methods in perturbated nonlinear operator equations.Comput. 32 (1984), 1-11. MR 0736257, 10.1007/BF02243015 |
| Reference:
|
[12] Voller R. L.: Monoton einschließende Newton-ähnliche Iterationsverfahren in halbgeordneten Räumen mit nicht notwendig regularem Kegel.Dissertation, Düsseldorf 1982. |
| Reference:
|
[13] Voller R. L.: Iterative Einschließung von Lösungen nichtlinearer Differentialgleichungen durch Newton-ähnliche Iterationsverfahren.Apl. Mat. 31 (1986), 1-18. MR 0836798 |
| Reference:
|
[14] Voss H.: Ein neues Verfahren zur Einschließung der Lösungen von Operatorgleichungen.Z. Angew. Math. Mech. 56 (1976), 218-219. Zbl 0341.65040, MR 0408240, 10.1002/zamm.19760560509 |
| . |
