Quasilinearization for the periodic boundary value problem for hybrid differential equation

• Autorzy: L. Hall , S. Hristova
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2004
• Tom: 2
• Numer: 2
• Strony: 250-259

Daty

wydano

2004-04-01

online

2004-04-01

Twórcy

autor

L. Hall

• University of Missouri-Rolla

autor

S. Hristova

• Denison University

Bibliografia

• [1] R. Bellman and R. Kalaba: Quasilinearization and Nonlinear Boundary Value Problems, Elsivier, New York, 1965.
• [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.
• [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
• [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.
• [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.
• [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
• [10] V. Lakshmikantham and A.S. Vatsala: Generalized Quasilinearization for Nonlinear Problems, Kluwer Academic Publishers, 1998.
• [11] A. Nerode and W. Kohn: Medels in Hybrid Systems, Lecture Notes in Computer Science, Vol. 36, Springer Verlag, Berlin, 1993.

Identyfikatory

DOI

10.2478/BF02476542