Legendre polynomials operational matrix method for solving fractional partial differential equations with variable coefficients
type: Item
instance of: scholarly article
title: Legendre polynomials operational matrix method for solving fractional partial differential equations with variable coefficients
zbMATH Open document ID: 1394.65114
DOI: 10.1155/2015/915195
author: Yongqiang Yang
author: Yunpeng Ma
author: Lifeng Wang
published in: Mathematical Problems in Engineering
publication date: 2018-08-27T00:00:00Z
review text: Summary: A numerical method for solving a class of fractional partial differential equations with variable coefficients based on Legendre polynomials is proposed. A fractional order operational matrix of Legendre polynomials is also derived. The initial equations are transformed into the products of several matrixes by using the operational matrix. A system of linear equations is obtained by dispersing the coefficients and the products of matrixes. Only a small number of Legendre polynomials are needed to acquire a satisfactory result. Results obtained using the scheme presented here show that the numerical method is very effective and convenient for solving fractional partial differential equations with variable coefficients.
Mathematics Subject Classification ID: 65M70
Mathematics Subject Classification ID: 35R11
zbMATH DE Number: 6927544
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2015/915195
OpenAlex ID: W2104251590
Wikidata QID: Q59120256
cites work: Q3538132
cites work: Existence and uniqueness for a nonlinear fractional differential equation
cites work: Nonlinear functional differential equations of arbitrary orders
cites work: Error estimate of the series solution to a class of nonlinear fractional differential equations
cites work: A study on the convergence of variational iteration method
cites work: Generalized differential transform method for solving a space- and time-fractional diffusion-wave equation
cites work: Generalized differential transform method: Application to differential equations of fractional order
cites work: A generalized differential transform method for linear partial differential equations of fractional order
cites work: A finite difference method for fractional partial differential equation
cites work: The second kind Chebyshev wavelet method for solving fractional differential equations
cites work: Haar Wavelet Operational Matrix Method for Solving Fractional Partial Differential Equations
cites work: The operational matrix formulation of the Jacobi tau approximation for space fractional diffusion equation
cites work: Block pulse operational matrix method for solving fractional partial differential equation
cites work: Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
cites work: A new operational matrix for solving fractional-order differential equations
cites work: Legendre wavelet method for numerical solutions of partial differential equations
cites work: Legendre expansion methods for the numerical solution of nonlinear 2D Fredholm integral equations of the second kind
description: scientific article; zbMATH DE number 6927544