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Generalized quasilinearization method for a second order three point boundary-value problem with nonlinear boundary conditions

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Author(s): Bashir Ahmad | Rahmat Ali Khan | Paul W. Eloe

Journal: Electronic Journal of Differential Equations
ISSN 1072-6691

Volume: 2002;
Issue: 90;
Start page: 1;
Date: 2002;
Original page

Keywords: Generalized quasilinearization | boundary value problem | nonlinear boundary conditions | quadratic and rapid convergence.

ABSTRACT
The generalized quasilinearization technique is applied to obtain a monotone sequence of iterates converging uniformly and quadratically to a solution of three point boundary value problem for second order differential equations with nonlinear boundary conditions. Also, we improve the convergence of the sequence of iterates by establishing a convergence of order $k$. Submitted March 14, 2002. Published October 22, 2002. Math Subject Classifications: 34B10, 34B15. Key Words: Generalized quasilinearization; boundary value problem; nonlinear boundary conditions; quadratic and rapid convergence.
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