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2013 An Efficient Higher-Order Quasilinearization Method for Solving Nonlinear BVPs
Eman S. Alaidarous, Malik Zaka Ullah, Fayyaz Ahmad, A.S. Al-Fhaid
J. Appl. Math. 2013: 1-11 (2013). DOI: 10.1155/2013/259371

Abstract

In this research paper, we present higher-order quasilinearization methods for the boundary value problems as well as coupled boundary value problems. The construction of higher-order convergent methods depends on a decomposition method which is different from Adomain decomposition method (Motsa and Sibanda, 2013). The reported method is very general and can be extended to desired order of convergence for highly nonlinear differential equations and also computationally superior to proposed iterative method based on Adomain decomposition because our proposed iterative scheme avoids the calculations of Adomain polynomials and achieves the same computational order of convergence as authors have claimed in Motsa and Sibanda, 2013. In order to check the validity and computational performance, the constructed iterative schemes are also successfully applied to bifurcation problems to calculate the values of critical parameters. The numerical performance is also tested for one-dimension Bratu and Frank-Kamenetzkii equations.

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Eman S. Alaidarous. Malik Zaka Ullah. Fayyaz Ahmad. A.S. Al-Fhaid. "An Efficient Higher-Order Quasilinearization Method for Solving Nonlinear BVPs." J. Appl. Math. 2013 1 - 11, 2013. https://doi.org/10.1155/2013/259371

Information

Published: 2013
First available in Project Euclid: 14 March 2014

zbMATH: 06950587
MathSciNet: MR3133968
Digital Object Identifier: 10.1155/2013/259371

Rights: Copyright © 2013 Hindawi

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