Atici, F. Merdivenci; Topal, S. Gulsan The generalized quasilinearization method and three point boundary value problems on time scales. (English) Zbl 1075.34006 Appl. Math. Lett. 18, No. 5, 577-585 (2005). 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. Cited in 12 Documents 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 Keywords:Time scales; Three-point boundary value problems; Lower and upper solutions; Convergence PDF BibTeX XML Cite \textit{F. M. Atici} and \textit{S. G. Topal}, Appl. Math. Lett. 18, No. 5, 577--585 (2005; Zbl 1075.34006) Full Text: DOI References: [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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.