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.
@article{bwmeta1.element.doi-10_2478_BF02476542, author = {L. Hall and S. Hristova}, title = {Quasilinearization for the periodic boundary value problem for hybrid differential equation}, journal = {Open Mathematics}, volume = {2}, year = {2004}, pages = {250-259}, zbl = {1069.34022}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_BF02476542} }
L. Hall; S. Hristova. Quasilinearization for the periodic boundary value problem for hybrid differential equation. Open Mathematics, Tome 2 (2004) pp. 250-259. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_BF02476542/
[1] R. Bellman and R. Kalaba: Quasilinearization and Nonlinear Boundary Value Problems, Elsivier, New York, 1965. | Zbl 0139.10702
[2] F.H. Clark, Yu.S. Ledayaev, R.I. Steru and P.R. Wolenski: Nonsmooth Analysis and Control Theory, Springer Verlag, New York, 1998.
[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.
[4] G. Ladde, V. Lakshmikantham and A. Vatsala: Monotone Iterative Techniques for Nonlinear Differential Equations, Pitman, Belmonth, 1985. | Zbl 0658.35003
[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 | Zbl 0806.34013
[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. | Zbl 0799.34012
[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. | Zbl 0855.34013
[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 | Zbl 0855.34011
[10] V. Lakshmikantham and A.S. Vatsala: Generalized Quasilinearization for Nonlinear Problems, Kluwer Academic Publishers, 1998. | Zbl 0997.34501
[11] A. Nerode and W. Kohn: Medels in Hybrid Systems, Lecture Notes in Computer Science, Vol. 36, Springer Verlag, Berlin, 1993.