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Title: Boundary value problems for ODEs (English)
Author: Jankowski, Tadeusz
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 53
Issue: 3
Year: 2003
Pages: 743-756
Summary lang: English
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Category: math
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Summary: We use the method of quasilinearization to boundary value problems of ordinary differential equations showing that the corresponding monotone iterations converge to the unique solution of our problem and this convergence is quadratic. (English)
Keyword: quasilinearization
Keyword: monotone iterations
Keyword: quadratic convergence
MSC: 34A45
MSC: 34B05
MSC: 34B08
MSC: 34B15
MSC: 34B99
idZBL: Zbl 1080.34511
idMR: MR2000066
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Date available: 2009-09-24T11:06:11Z
Last updated: 2020-07-03
Stable URL: http://hdl.handle.net/10338.dmlcz/127836
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Reference: [2] R. Bellman and R. Kalaba: Quasilinearization and Nonlinear Boundary Value Problems.American Elsevier, New York, 1965. MR 0178571
Reference: [3] G. S. Ladde V. Lakshmikantham and A. S. Vatsala: Monotone Iterative Techniques for Nonlinear Differential Equations.Pitman, Boston, 1985. MR 0855240
Reference: [4] V. Lakshmikantham: Further improvements of generalized quasilinearization method.Nonlinear Anal. 27 (1996), 223–227. MR 1389479, 10.1016/0362-546X(94)00281-L
Reference: [5] V. Lakshmikantham, S. Leela and S. Sivasundaram: Extensions of the method of quasilinearization.J.  Optim. Theory Appl. 87 (1995), 379–401. MR 1358749, 10.1007/BF02192570
Reference: [6] 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: [7] 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: [8] V. Lakshmikantham and A. S. Vatsala: Generalized Quasilinearization for Nonlinear Problems.Kluwer Academic Publishers, Dordrecht, Boston, London, 1998. MR 1640601
Reference: [9] 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
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