# Quasilinearization for the periodic boundary value problem for hybrid differential equation

Open Mathematics (2004)

- Volume: 2, Issue: 2, page 250-259
- ISSN: 2391-5455

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topL. Hall, and S. Hristova. "Quasilinearization for the periodic boundary value problem for hybrid differential equation." Open Mathematics 2.2 (2004): 250-259. <http://eudml.org/doc/268719>.

@article{L2004,

abstract = {The method of quasilinearization for a periodic boundary value problem for nonlinear hybrid differential equations is studied. It is shown that the convergence is quadratic.},

author = {L. Hall, S. Hristova},

journal = {Open Mathematics},

keywords = {hybrid differential equations; periodic boundary value problem; quasilinearization; quadratic convergence; MSC (2000); 34K10; 34B15; 34K25; hybrid systems},

language = {eng},

number = {2},

pages = {250-259},

title = {Quasilinearization for the periodic boundary value problem for hybrid differential equation},

url = {http://eudml.org/doc/268719},

volume = {2},

year = {2004},

}

TY - JOUR

AU - L. Hall

AU - S. Hristova

TI - Quasilinearization for the periodic boundary value problem for hybrid differential equation

JO - Open Mathematics

PY - 2004

VL - 2

IS - 2

SP - 250

EP - 259

AB - The method of quasilinearization for a periodic boundary value problem for nonlinear hybrid differential equations is studied. It is shown that the convergence is quadratic.

LA - eng

KW - hybrid differential equations; periodic boundary value problem; quasilinearization; quadratic convergence; MSC (2000); 34K10; 34B15; 34K25; hybrid systems

UR - http://eudml.org/doc/268719

ER -

## References

top- [1] R. Bellman and R. Kalaba: Quasilinearization and Nonlinear Boundary Value Problems, Elsivier, New York, 1965. Zbl0139.10702
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- [3] L.J. Grimm and L.M. Hall: “Differential Inequalities and Boundary Problems for Functional-Differential Equations”, In: Simposium on Ordinary Differential Equations, Lecture Notes in Mathematics, Vol. 312, Springer Verlag, Berlin, pp. 41–53.
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- [5] V. Lakshmikantham, “Extension of the method of quasilinearization”, J. Optim. Theor. Applic., Vol. 82, (1994), pp. 315–321. http://dx.doi.org/10.1007/BF02191856 Zbl0806.34013
- [6] V. Lakshmikantham and X.Z. Liu: “Impulsive hybrid systems and stability theory”, Intern. J. Nonlinear Diff. Eqns, Vol. 5, (1999), pp. 9–17.
- [7] V. Lakshmikantham and S. Malek: Generalized quasilinearization, Nonlinear World, 1, (1994), 59–63. Zbl0799.34012
- [8] V. Lakshmikantham and J.J. Nieto: “Generalized quasilinearization for nonlinear first order ordinary differential equations”, Nonlinear Times and Digest, Vol. 2, (1995), pp. 1–9. Zbl0855.34013
- [9] V. Lakshmikantham, N. Shahzad and J.J. Nieto: “Method of generalized quasilinearization for periodic boundary value problems, Nonlinear Analysis, Vol. 27, (1996), pp. 143–151. http://dx.doi.org/10.1016/0362-546X(95)00021-M Zbl0855.34011
- [10] V. Lakshmikantham and A.S. Vatsala: Generalized Quasilinearization for Nonlinear Problems, Kluwer Academic Publishers, 1998. Zbl0997.34501
- [11] A. Nerode and W. Kohn: Medels in Hybrid Systems, Lecture Notes in Computer Science, Vol. 36, Springer Verlag, Berlin, 1993.

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