| Title:
|
On Urabe's application of Newton's method to nonlinear boundary value problems (English) |
| Author:
|
Agarwal, Ravi P. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
20 |
| Issue:
|
3 |
| Year:
|
1984 |
| Pages:
|
113-123 |
| . |
| Category:
|
math |
| . |
| MSC:
|
34B15 |
| idZBL:
|
Zbl 0572.34020 |
| idMR:
|
MR784862 |
| . |
| Date available:
|
2008-06-06T06:13:31Z |
| Last updated:
|
2012-05-09 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107194 |
| . |
| Reference:
|
[1] R. P. Agarwal: Iterative methods for the system of second order boundary value problems.J. Math. Phys. Sci. 11 (1977), 209-218. MR 0461924 |
| Reference:
|
[2] R. P. Agarwal: Component-wise convergence in quasilinearization.Proc. Indian Acad. Sci. Sec. A. 86 (1977), 519-529. MR 0492473 |
| Reference:
|
[3] R. P. Agarwal: On periodic solutions of nonlinear second order differential systems.J. Comp. Appl. Math. 5 (1979), 117-123. Zbl 0407.34021, MR 0536248 |
| Reference:
|
[4] R. P. Agarwal, Jaromír Vosmanský: Two-point boundary value problems for second order systems.Arch. Math. (Brno), 19 (1983), 1-8. MR 0724304 |
| Reference:
|
[5] R. P. Agarwal: Contraction and approximate contraction with an application to multi-point boundary value problems.J. Comp. Appl. Math. 9 (1983), 315-325. Zbl 0546.65060, MR 0729235 |
| Reference:
|
[6] G. Anichini: Nonlinear problems for systems of differential equations.Nonlinear Analysis. Theory, Methods and Applications, 1 (1977), 691-699. Zbl 0388.34011, MR 0592963 |
| Reference:
|
[7] S. R. Bernfeld, V. Lakshmikantham: An Introduction to Nonlinear Boundary Value Problems.Academic Press, New York, 1974. Zbl 0286.34018, MR 0445048 |
| Reference:
|
[8] L. Collatz: Functional Analysis and Numerical Mathematics.Academic Press, New York, 1974. MR 0205126 |
| Reference:
|
[9] R. Conti: Recent trends in the theory of boundary value problems for ordinary differential equations.Boll. UMI, 22 (1967), 135-178. Zbl 0154.09101, MR 0218650 |
| Reference:
|
[10] P. L. Falb, J. L. de Jong: Some Successive Approximation Methods in Control and Oscillation Theory.Academic Press, New York, 1969. Zbl 0202.09603, MR 0264855 |
| Reference:
|
[11] A. Perov, A. Kibenko: On a certain general method for investigation of boundary value problems.Izv. Akad. Nauk SSSR 30 (1966), 249-264. MR 0196534 |
| Reference:
|
[12] J. Schröder: Das Iterationsverfahren bei verallgemeinertem Abstandsbegriff.Math. Z. 60 (1956), 111-116. MR 0083816 |
| Reference:
|
[13] M. Urabe: An existence theorem for multi-point boundary value problems.Funkcialaj Ekvacioj, 9 (1966), 43-60. Zbl 0168.06502, MR 0209558 |
| Reference:
|
[14] M. Urabe: The Newton method and its applications.Proc. US-Japan seminar on differential and functional equations, (1967), 383-410. MR 0223628 |
| Reference:
|
[15] M. Urabe: Component-wise error analysis of iterative methods practiced on a floating-point system.Mem. Fac. Sci. Kyushu Univ. Ser. A. 27 (1973), 23-64. Zbl 0277.65034, MR 0323099 |
| Reference:
|
[16] M. Urabe: A posteriori component-wise error estimation of approximate solutions to nonlinear equations.Lecture notes in Computer science 29, Interval Mathematics, Springer-Verlag (1975), 99-117. Zbl 0306.65031 |
| Reference:
|
[17] M. Urabe: On the Newton method to solve problems of the least squares type for ordinary differential equations.Proc. Int. Symp. Dynamical Systems, Providence, (1974), 1-7. MR 0375791 |
| Reference:
|
[18] M. Urabe: On the Newton method to solve problems of the least squares type for ordinary differential equations.Mem. Fac. Sci. Kyushu Univ., Ser. A, 29 (1975), 173-183. Zbl 0357.65055, MR 0375791 |
| . |
