Title:
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Multipoint boundary value problems for ODEs. Part II (English) |
Author:
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Jankowski, Tadeusz |
Language:
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English |
Journal:
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Czechoslovak Mathematical Journal |
ISSN:
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0011-4642 (print) |
ISSN:
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1572-9141 (online) |
Volume:
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54 |
Issue:
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4 |
Year:
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2004 |
Pages:
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843-854 |
Summary lang:
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English |
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Category:
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math |
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Summary:
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We apply the method of quasilinearization to multipoint boundary value problems for ordinary differential equations showing that the corresponding monotone iterations converge to the unique solution of our problem and this convergence is quadratic. (English) |
Keyword:
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quasilinearization |
Keyword:
|
monotone iterations |
Keyword:
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quadratic convergence |
Keyword:
|
multipoint boundary value problems |
MSC:
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34A45 |
MSC:
|
34B10 |
MSC:
|
34B99 |
idZBL:
|
Zbl 1080.34512 |
idMR:
|
MR2099998 |
. |
Date available:
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2009-09-24T11:18:09Z |
Last updated:
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2020-07-03 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/127934 |
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Reference:
|
[1] R. A. Agarwal, D. O’Regan and P. J. Y. Wong: Positive Solutions of Differential Difference and Integral Equations.Kluwer Academic Publishers, Dordrecht, 1999. MR 1680024 |
Reference:
|
[2] R. Bellman: Methods of Nonlinear Analysis, Vol. II.Academic Press, New York, 1973. Zbl 0265.34002, MR 0381408 |
Reference:
|
[3] R. Bellman and R. Kalaba: Quasilinearization and Nonlinear Boundary Value Problems.American Elsevier, New York, 1965. MR 0178571 |
Reference:
|
[4] S. Heikkilä and V. Lakshmikantham: Monotone Iterative Techniques for Discontinuous Nonlinear Differential Equations.Marcel Dekker, New York, 1994. MR 1280028 |
Reference:
|
[5] T. Jankowski: Boundary value problems for ODEs.Czechoslovak Math. J. 53 (2003), 743–756. Zbl 1080.34511, MR 2000066, 10.1023/B:CMAJ.0000024516.59951.33 |
Reference:
|
[6] T. Jankowski: Multipoint boundary value problems for ODEs. Part I.Appl. Anal. 80 (2001), 395–407. MR 1914690, 10.1080/00036810108841001 |
Reference:
|
[7] G. S. Ladde, V. Lakshmikantham and A. S. Vatsala: Monotone Iterative Techniques for Nonlinear Differential Equations.Pitman, Boston, 1985. MR 0855240 |
Reference:
|
[8] V. Lakshmikantham: Further improvements of generalized quasilinearization method.Nonlinear Anal. 27 (1996), 223–227. MR 1389479, 10.1016/0362-546X(94)00281-L |
Reference:
|
[9] V. Lakshmikantham, S. Leela and S. Sivasundaram: Extensions of the method of quasilinearization.J. Optimization Theory Appl. 87 (1995), 379–401. MR 1358749, 10.1007/BF02192570 |
Reference:
|
[10] V. Lakshmikantham, N. Shahzad and J. J. Nieto: Methods of generalized quasilinearization for periodic boundary value problems.Nonlinear Anal. 27 (1996), 143–151. MR 1389474, 10.1016/0362-546X(95)00021-M |
Reference:
|
[11] V. Lakshmikantham and N. Shahzad: Further generalization of generalized quasilinearization method.J. Appl. Math. Stoch. Anal. 7 (1994), 545–552. MR 1310927, 10.1155/S1048953394000420 |
Reference:
|
[12] V. Lakshmikantham and A. S. Vatsala: Generalized Quasilinearization for Nonlinear Problems.Kluwer Academic Publishers, Dordrecht, 1998. MR 1640601 |
Reference:
|
[13] D. O’Regan and M. Meehan: Existence Theory for Nonlinear Integral and Integrodifferential Equations.Kluwer Academic Publishers, Dordrecht, 1998. MR 1646557 |
Reference:
|
[14] M. Ronto and A. M. Samoilenko: Numerical-Analytic Methods in the Theory of Boundary-Value Problems.World Scientific, Singapore, 2000. MR 1781545 |
Reference:
|
[15] V. Šeda: A remark to quasilinearization.J. Math. Anal. Appl. 23 (1968), 130–138. MR 0226850, 10.1016/0022-247X(68)90121-2 |
Reference:
|
[16] Y. Yin: Remarks on first order differential equations with anti-periodic boundary conditions.Nonlinear Times Digest 2 (1995), 83–94. Zbl 0832.34018, MR 1333336 |
Reference:
|
[17] Y. Yin: Monotone iterative technique and quasilinearization for some anti-periodic problems.Nonlinear World 3 (1996), 253–266. Zbl 1013.34015, MR 1390017 |
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