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The generalized quasilinearization method and three point boundary value problems on time scales. (English) Zbl 1075.34006
Summary: We study the convergence of monotone sequences of iterates for nonlinear second-order dynamic equations with three-point boundary conditions on time scales. We prove that it is possible to construct two sequences converging to the unique solution of the three-point boundary value problem from above and below with high rate of convergence.

MSC:
34A45 Theoretical approximation of solutions to ordinary differential equations
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
39A12 Discrete version of topics in analysis
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[1] Bohner, M.; Peterson, A., Dynamic equations on time scales, an introduction with applications, (2001), Birkhäuser · Zbl 0978.39001
[2] Bohner, M.; Peterson, A., Advances in dynamic equations on time scales, (2003), Birkhäuser Boston · Zbl 1025.34001
[3] Ahmad, B.; Khan, R.A.; Eloe, P.W., Generalized quasilinearization method for a second three point boundary value problem with nonlinear boundary conditions, Electron J. differential equations, 90, 1-12, (2002) · Zbl 1027.34013
[4] Atici, F.M.; Guseinov, G.Sh., On green’s functions and positive solutions for boundary value problems on time scales, J. comput. appl. math., 141, 1-2, 75-99, (2002) · Zbl 1007.34025
[5] Atici, F.M.; Eloe, P.W.; Kaymakcalan, B., The quasilinearization method for boundary value problems on time scales, J. math. anal. appl., 276, 357-372, (2002) · Zbl 1021.34006
[6] Cabada, A.; Nieto, J.J., Quasilinearization and rate of convergence for higher-order nonlinear periodic boundary value problems, J. optim. theory appl., 108, 97-107, (2001) · Zbl 0976.34015
[7] Eloe, P.W.; Gao, Y., The method of quasilinearization and a three-point boundary value problem, J. Korean math. soc., 39, 2, 319-330, (2002) · Zbl 1012.34014
[8] Lakshmikantham, V.; Vatsala, A.S., Generalized quasilinearization and nonlinear problems, (1998), Kluwer publications · Zbl 0997.34501
[9] Atici, F.M.; Topal, S.G., Three point boundary value problems on time scales, Dynam. systems appl., 13, 3-4, 327-337, (2004) · Zbl 1069.39018
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