An efficient higher-order quasilinearization method for solving nonlinear BVPs
type: Item
instance of: scholarly article
title: An efficient higher-order quasilinearization method for solving nonlinear BVPs
zbMATH Open document ID: 1397.34046
DOI: 10.1155/2013/259371
author: Malik Zaka Ullah
author: Fayyaz Ahmad
author: Eman Alaidarous
author: A. Al-Fhaid
published in: Journal of Applied Mathematics
publication date: 2018-10-10T00:00:00Z
review text: Summary: 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 [\textit{S. S. Motsa} and \textit{P. Sibanda}, Numer. Algorithms 63, No. 3, 399--417 (2013; Zbl 1271.65115)]. 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 [loc. cit.]. 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.
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 65Y20
zbMATH DE Number: 6950587
Wikidata QID: Q59002425
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/259371
OpenAlex ID: W2156565866
description: scientific article; zbMATH DE number 6950587