A fourth-order non-uniform mesh optimal B-spline collocation method for solving a strongly nonlinear singular boundary value problem describing electrohydrodynamic flow of a fluid
type: Item
instance of: scholarly article
title: A fourth-order non-uniform mesh optimal B-spline collocation method for solving a strongly nonlinear singular boundary value problem describing electrohydrodynamic flow of a fluid
zbMATH Open document ID: 1445.65028
author: Pradip Roul
published in: Applied Numerical Mathematics
publication date: 2020-04-07T00:00:00Z
review text: The author develops and implements a very interesting fourth-order numerical method - a nonuniform mesh optimal cubic B-spline collocation method - for the numerical solution of a strongly nonlinear singular boundary value problem. This method consists of five steps: \begin{itemize} \item L'Hôpital's rule is used to overcome the singularity behavior at the point \(r = 0\). \item Newton's method is used to linearize the resulting problem obtained in step 1. \item A grading function is appropriately chosen in order to generate a nonuniform partition over the solution domain. \item Cubic B-spline basis functions on nonuniform partition are constructed. \item An optimal B-spline collocation method on nonuniform mesh is designed to approximate the solution of the considered problem using the basis functions obtained in the previous step. \end{itemize} The convergence analysis of the proposed method is discussed.
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 65L60
Mathematics Subject Classification ID: 76W05
zbMATH DE Number: 7188163
zbMATH Keywords: electrohydrodynamic flows
zbMATH Keywords: grading function
zbMATH Keywords: Hartmann electric number
zbMATH Keywords: nonlinearity
zbMATH Keywords: non-uniform partition
zbMATH Keywords: B-spline collocation method
reviewed by: Antonio López-Carmona
MaRDI profile type: Publication
full work available at URL: j.apnum.2020.03.018
OpenAlex ID: W3011866149
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DOI: 10.1016/J.APNUM.2020.03.018
description: scientific article; zbMATH DE number 7188163