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2014 Superlinear convergence via mixed generalized quasilinearization method and generalized monotone method
Vinchencia Anderson, Courtney Bettis, Shala Brown, Jacqkis Davis, Naeem Tull-Walker, Vinodh Chellamuthu, Aghalaya Vatsala
Involve 7(5): 699-712 (2014). DOI: 10.2140/involve.2014.7.699


The method of upper and lower solutions guarantees the interval of existence of nonlinear differential equations with initial conditions. To compute the solution on this interval, we need coupled lower and upper solutions on the interval of existence. We provide both theoretical as well as numerical methods to compute coupled lower and upper solutions by using a superlinear convergence method. Further, we develop monotone sequences which converge uniformly and monotonically, and with superlinear convergence, to the unique solution of the nonlinear problem on this interval. We accelerate the superlinear convergence by means of the Gauss–Seidel method. Numerical examples are developed for the logistic equation. Our method is applicable to more general nonlinear differential equations, including Riccati type differential equations.


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Vinchencia Anderson. Courtney Bettis. Shala Brown. Jacqkis Davis. Naeem Tull-Walker. Vinodh Chellamuthu. Aghalaya Vatsala. "Superlinear convergence via mixed generalized quasilinearization method and generalized monotone method." Involve 7 (5) 699 - 712, 2014.


Received: 15 September 2013; Revised: 22 November 2013; Accepted: 24 November 2013; Published: 2014
First available in Project Euclid: 20 December 2017

zbMATH: 1301.34018
MathSciNet: MR3245845
Digital Object Identifier: 10.2140/involve.2014.7.699

Primary: 34A12
Secondary: 34A34

Keywords: coupled lower and upper solutions , Superlinear convergence

Rights: Copyright © 2014 Mathematical Sciences Publishers


Vol.7 • No. 5 • 2014
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