| Title:
|
Discrete evolutions: Convergence and applications (English) |
| Author:
|
Bohl, Erich |
| Author:
|
Schropp, Johannes |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
38 |
| Issue:
|
4 |
| Year:
|
1993 |
| Pages:
|
266-280 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove a convergence result for a time discrete process of the form $x(t+h)-x(t)=hV(h,x(t+\alpha_1(t)h), ..., x(t+\alpha_L(t)h)) t=T+jh, j=0, ..., \sigma(h)-1$ under weak conditions on the function $V$. This result is a slight generalization of the convergence result given in [5].Furthermore, we discuss applications to minimizing problems, boundary value problems and systems of nonlinear equations. (English) |
| Keyword:
|
discrete processes |
| Keyword:
|
continuous processes |
| Keyword:
|
convergence of discretisations |
| Keyword:
|
boundary value problems |
| Keyword:
|
minimizing problems |
| Keyword:
|
Newton's iteration and Newton's flow |
| Keyword:
|
discrete evolutions |
| Keyword:
|
systems of nonlinear equations |
| MSC:
|
65H10 |
| MSC:
|
65K10 |
| MSC:
|
65L20 |
| MSC:
|
65L99 |
| MSC:
|
65Q05 |
| MSC:
|
93C55 |
| idZBL:
|
Zbl 0823.65064 |
| idMR:
|
MR1228508 |
| DOI:
|
10.21136/AM.1993.104555 |
| . |
| Date available:
|
2008-05-20T18:45:55Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104555 |
| . |
| Reference:
|
[1] Boggs P. Т.: The solution of nonlinear systems of equations by A-stable integration techniques.SIAM J. Numer. Anal. 8 (1971), 767-785. Zbl 0223.65047, MR 0297121, 10.1137/0708071 |
| Reference:
|
[2] Bohl E.: Finite Modelle gewöhnlicher Randwertaufgaben.Teubner Studienbücher, B.G. Teubner, 1981. Zbl 0472.65070, MR 0633643 |
| Reference:
|
[3] Bohl E.: Mathematische Grundlagen für die Modellierung biologischer Vorgänge.Springer Hochschultexte, Springer, 1987. Zbl 0643.92001, MR 1032759 |
| Reference:
|
[4] Bohl E.: Mathematik und Leben, Die Frage nach dem Leben.Serie Piper (Fischer, E.P., Mainzer, K., eds.), 1990, pp. 233-263. |
| Reference:
|
[5] Bohl E.: On the convergence of time-discrete processes.to appear in ZAMM 1993. MR 1302474 |
| Reference:
|
[6] Collet P., Eckmann J. P.: Iterated Maps on the Interval as dynamical Systems.Progress in Physics, Vol. 1, Basel. Zbl 0458.58002 |
| Reference:
|
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| Reference:
|
[8] Dennis J. E., Schnabel R. B.: Numerical Methods for Unconstrained Optimisation and Nonlinear Equations.Prentice-Hall Inc., Engelwood Cliffs, New Jersey, 1983. MR 0702023 |
| Reference:
|
[9] Gill P. E., Murray W., Wright M. H.: Practical Optimization.Academic Press, London, New York, 1981. Zbl 0503.90062, MR 0634376 |
| Reference:
|
[10] Grigorieff R. D.: Numerik gewöhnlicher Differentialgleichungen 1, 2.Teubner Studienbücher, B.C. Teubner, 1972. MR 0468207 |
| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
|
[15] Schropp J.: Global dynamics of Newton's flow.in preparation. |
| Reference:
|
[16] Werner J.: Numerische Mathematik I.Vieweg, Braunschweig/Wiesbaden, 1992. |
| Reference:
|
[17] Wissel C.: Theoretische Ökologie.Springer, Berlin, Heidelberg, New York, 1989. |
| . |
