Legendre collocation method for solving nonlinear differential equations
type: Item
instance of: scholarly article
title: Legendre collocation method for solving nonlinear differential equations
zbMATH Open document ID: 1396.65124
author: Aysun Güner
author: Salih Yalçınbaş
published in: Mathematical \& Computational Applications
publication date: 2018-07-05T00:00:00Z
review text: Summary: In this study, a matrix method based on Legendre collocation points on interval \([-1,1]\) is proposed for the approximate solution of the some first order nonlinear ordinary differential equations with the mixed conditions in terms of Legendre polynomials. The method by means of Legendre collocation points, transforms the differential equation to a matrix equation which corresponds to a system of nonlinear algebraic equations with unknown Legendre coefficients. Also, the method can be used for solving Riccati equation. The numerical results show the effectuality of the method for this type of equations. Comparisons are made between the obtained solution and the exact solution.
Mathematics Subject Classification ID: 65L60
zbMATH DE Number: 6898868
zbMATH Keywords: nonlinear ordinary differential equations
zbMATH Keywords: Legendre polynomials and series
zbMATH Keywords: Legendre collocation points
zbMATH Keywords: Legendre collocation method
MaRDI profile type: Publication
full work available at URL: mca18030521
OpenAlex ID: W2183150594
DOI: 10.3390/MCA18030521
description: scientific article; zbMATH DE number 6898868