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Keywords:
quasilinearization; monotone iterations; quadratic convergence
quasilinearization; monotone iterations; quadratic convergence
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.
References:
[1] R. Bellman: Methods of Nonlinear Analysis, Vol. II. Academic Press, New York, 1973. MR 0381408 | Zbl 0265.34002
[2] R. Bellman and R. Kalaba: Quasilinearization and Nonlinear Boundary Value Problems. American Elsevier, New York, 1965. MR 0178571
[3] G. S. Ladde V. Lakshmikantham and A. S. Vatsala: Monotone Iterative Techniques for Nonlinear Differential Equations. Pitman, Boston, 1985. MR 0855240
[4] V. Lakshmikantham: Further improvements of generalized quasilinearization method. Nonlinear Anal. 27 (1996), 223–227. DOI 10.1016/0362-546X(94)00281-L | MR 1389479
[5] V. Lakshmikantham, S. Leela and S. Sivasundaram: Extensions of the method of quasilinearization. J. Optim. Theory Appl. 87 (1995), 379–401. DOI 10.1007/BF02192570 | MR 1358749
[6] V. Lakshmikantham, N. Shahzad and J. J. Nieto: Methods of generalized quasilinearization for periodic boundary value problems. Nonlinear Anal. 27 (1996), 143–151. DOI 10.1016/0362-546X(95)00021-M | MR 1389474
[7] V. Lakshmikantham and N. Shahzad: Further generalization of generalized quasilinearization method. J. Appl. Math. Stoch. Anal. 7 (1994), 545–552. DOI 10.1155/S1048953394000420 | MR 1310927
[8] V. Lakshmikantham and A. S. Vatsala: Generalized Quasilinearization for Nonlinear Problems. Kluwer Academic Publishers, Dordrecht, Boston, London, 1998. MR 1640601
[9] Y. Yin: Remarks on first order differential equations with anti-periodic boundary conditions. Nonlinear Times Digest 2 (1995), 83–94. MR 1333336 | Zbl 0832.34018
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