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Functional differential equations. (English) Zbl 1023.34070

Summary: The method of quasilinearization is a well-known technique for obtaining approximate solutions to nonlinear differential equations. Here, the author applies this technique to functional-differential problems. It is shown that linear iterations converge to the unique solution and this convergence is superlinear.

MSC:

34K28 Numerical approximation of solutions of functional-differential equations (MSC2010)
34K05 General theory of functional-differential equations
34A45 Theoretical approximation of solutions to ordinary differential equations
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References:

[1] R. Bellman: Methods of Nonlinear Analysis, Vol. I. Academic Press, New York, 1973. · Zbl 0265.34002
[2] R. Bellman and R. Kalaba: Quasilinearization and Nonlinear Boundary Value Problems. American Elsevier, New York, 1965. · Zbl 0139.10702
[3] J. K. Hale and S. M. V. Lunel: Introduction to Functional Differential Equations. Springer-Verlag, New York, Berlin, 1993.
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[5] G. S. Ladde, V. Lakshmikantham and A. S. Vatsala: Monotone Iterative Techniques for Nonlinear Differential Equations. Pitman, Boston, 1985. · Zbl 0658.35003
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[7] V. Lakshmikantham and A. S. Vatsala: Generalized Quasilinearization for Nonlinear Problems. Kluwer Academic Publishers, Dordrecht-Boston-London, 1998. · Zbl 0997.34501
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