A numerical approach based on Taylor polynomials for solving a class of nonlinear differential equations
type: Item
instance of: scholarly article
title: A numerical approach based on Taylor polynomials for solving a class of nonlinear differential equations
zbMATH Open document ID: 1427.65120
DOI: 10.1155/2018/8256932
author: Xianqiang Yang
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: In this study, a matrix method based on Taylor polynomials and collocation points is presented for the approximate solution of a class of nonlinear differential equations, which have many applications in mathematics, physics and engineering. By means of matrix forms of the Taylor polynomials and their derivatives, the technique we have used reduces the solution of the nonlinear equation with mixed conditions to the solution of a matrix equation which corresponds to a system of nonlinear algebraic equations with the unknown Taylor coefficients. On the other hand, to illustrate the validity and applicability of the method, some numerical examples together with residual error analysis are performed and the obtained results are compared with the existing results in literature.
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 34A45
zbMATH DE Number: 7019579
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/8256932
OpenAlex ID: W2891937523
cites work: Q5562204
cites work: Q4040206
cites work: Q4001253
cites work: A numerical approach for the solution of a class of singular boundary value problems arising in physiology
cites work: A hybrid approach to parameter identification of linear delay differential equations involving multiple delays
cites work: Parameter identification of linear multi-delay systems via a hybrid of block-pulse functions and Taylor’s polynomials
cites work: A novel expansion iterative method for solving linear partial differential equations of fractional order
cites work: A general form of the generalized Taylor's formula with some applications
cites work: A novel representation of the exact solution for differential algebraic equations system using residual power-series method
cites work: A new numerical algorithm for the Abel equation of the second kind
cites work: Numerical solution of Duffing equation by using an improved Taylor matrix method
cites work: On the solution of the Riccati equation by the Taylor matrix method
cites work: Hybrid Euler-Taylor matrix method for solving of generalized linear Fredholm integro-differential difference equations
cites work: A new approach to numerical solution of nonlinear Klein-Gordon equation
cites work: Q5743574
cites work: Analytical approximations and Padé approximants for Volterra's population model
description: scientific article; zbMATH DE number 7019579