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Article

Keywords:
quasilinearization; monotone iterations; quadratic convergence
Summary:
The method of quasilinearization is a well–known technique for obtaining approximate solutions of nonlinear differential equations. This method has recently been generalized and extended using less restrictive assumptions so as to apply to a larger class of differential equations. In this paper, we use this technique to nonlinear differential problems.
References:
[1] Bellman, R.: Methods of Nonlinear Analysis. Vol. II, Academic Press, New York 1973. MR 0381408 | Zbl 0265.34002
[2] Bellman, R. and Kalaba, R.: Quasilinearization and Nonlinear Boundary Value Problems. American Elsevier, New York 1965. MR 0178571
[3] Jankowski, T. and Lakshmikantham, V.: Monotone iterations for differential equations with a parameter. J. Appl. Math. Stoch. Anal. 10 (1997), 273–278. MR 1468122
[4] Jankowski, T. and McRae, F. A.: An extension of the method of quasilinearization for differential problems with a parameter. Nonlinear Stud. 6 (1999), 21–44. MR 1691903
[5] Ladde, G. S., Lakshmikantham, V. and Vatsala, A. S.: Monotone Iterative Techniques for Nonlinear Differential Equations. Pitman 1985. MR 0855240
[6] Lakshmikantham, V. and Malek, S.: Generalized quasilenearization. Nonlinear World 1 (1994), 59–63. MR 1282859
[7] Lakshmikantham, V., Leela, S. and Sivasundaram, S.: Extensions of the Method of Quasilinearization. J. Optimization Theory Appl. Vol. 87 (1995), 379–401. MR 1358749
[8] Lakshmikantham, V. and Vatsala, A. S.: Generalized Quasilinearization for Nonlinear Problems. Kluwer Academic Publishers, Dordrecht 1998. MR 1640601
[9] Lakshmikantham, V., Leela, S. and McRae, F. A.: Improved Generalized Quasilinearization Method. Nonlinear Analysis 24 (1995), 1627–1637. MR 1328588
[10] Lakshmikantham, V. and Shahzad, N.: Further Generalization of Generalized Quasilinearization Method. J. Appl. Math. Stoch. Anal. 7 (1994), 545–552. MR 1310927
[11] Shahzad, N. and Vatsala, A. S.: An Extension of the Method of Generalized Quasilinearization for Second Order Boundary Value Problems. Appl. Anal. 58 (1995), 77–83. MR 1384590
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