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- W2023794043 abstract "We apply the generalized quasilinearization method to a second order three-point boundary value problem involving mixed nonlinear boundary conditions and obtain a monotone sequence of approximate solutions converging to the unique solution of the problem possessing a convergence of order k(k� 2). 1. Introduction. The method of quasilinearization developed by Bellman and Kalaba (1) and generalized by Lakshmikantham (2-3) later on, has been studied and extended in several diverse disciplines. In fact, it is generating a rich history and an extensive bibliography can be found in (4-10). Multi-point nonlinear boundary value problems, which refer to a different family of boundary conditions in the study of disconjugacy theory (11), have been addressed by many authors, for example, see (12-14). In particular, Eloe and Gao (15) dis- cussed the quasilinearization method for a three-point boundary value problem. In this paper, we study the generalized quasilinearization method for a second order three-point boundary value problem with mixed nonlinear boundary conditions. In fact, a sequence of approximate solutions converging monotonically to a solution of the nonlinear three-point problem with the order of convergence k(k ≥ 2) has been presented." @default.
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- W2023794043 date "2004-01-01" @default.
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- W2023794043 title "A Second Order Three-Point Boundary Value Problem with Mixed Nonlinear Boundary Conditions" @default.
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- W2023794043 doi "https://doi.org/10.4310/maa.2004.v11.n2.a7" @default.
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