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Title: Multipoint boundary value problems for ODEs. Part II (English)
Author: Jankowski, Tadeusz
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 54
Issue: 4
Year: 2004
Pages: 843-854
Summary lang: English
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Category: math
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Summary: 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: quasilinearization
Keyword: monotone iterations
Keyword: quadratic convergence
Keyword: multipoint boundary value problems
MSC: 34A45
MSC: 34B10
MSC: 34B99
idZBL: Zbl 1080.34512
idMR: MR2099998
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Date available: 2009-09-24T11:18:09Z
Last updated: 2020-07-03
Stable URL: 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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