Legendre Polynomials Operational Matrix Method for Solving Fractional Partial Differential Equations with Variable Coefficients

Legendre Polynomials Operational Matrix Method for Solving Fractional Partial Differential Equations with Variable Coefficients

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...

Full description

Bibliographic Details
Main Authors: Yongqiang Yang, Yunpeng Ma, Lifeng Wang
Format: Article
Language:English
Published: Hindawi Limited 2015-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2015/915195
id doaj-9772817039ed4070b71ee7216d27784d
record_format Article
spelling doaj-9772817039ed4070b71ee7216d27784d2020-11-24T20:56:51ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472015-01-01201510.1155/2015/915195915195Legendre Polynomials Operational Matrix Method for Solving Fractional Partial Differential Equations with Variable CoefficientsYongqiang Yang0Yunpeng Ma1Lifeng Wang2School of Aeronautic Science and Technology, Beihang University, Beijing 100191, ChinaSchool of Aeronautic Science and Technology, Beihang University, Beijing 100191, ChinaSchool of Aeronautic Science and Technology, Beihang University, Beijing 100191, ChinaA 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.http://dx.doi.org/10.1155/2015/915195
collection DOAJ
language English
format Article
sources DOAJ
author Yongqiang Yang
Yunpeng Ma
Lifeng Wang
spellingShingle Yongqiang Yang
Yunpeng Ma
Lifeng Wang
Legendre Polynomials Operational Matrix Method for Solving Fractional Partial Differential Equations with Variable Coefficients
Mathematical Problems in Engineering
author_facet Yongqiang Yang
Yunpeng Ma
Lifeng Wang
author_sort Yongqiang Yang
title Legendre Polynomials Operational Matrix Method for Solving Fractional Partial Differential Equations with Variable Coefficients
title_short Legendre Polynomials Operational Matrix Method for Solving Fractional Partial Differential Equations with Variable Coefficients
title_full Legendre Polynomials Operational Matrix Method for Solving Fractional Partial Differential Equations with Variable Coefficients
title_fullStr Legendre Polynomials Operational Matrix Method for Solving Fractional Partial Differential Equations with Variable Coefficients
title_full_unstemmed Legendre Polynomials Operational Matrix Method for Solving Fractional Partial Differential Equations with Variable Coefficients
title_sort legendre polynomials operational matrix method for solving fractional partial differential equations with variable coefficients
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2015-01-01
description 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.
url http://dx.doi.org/10.1155/2015/915195
work_keys_str_mv AT yongqiangyang legendrepolynomialsoperationalmatrixmethodforsolvingfractionalpartialdifferentialequationswithvariablecoefficients
AT yunpengma legendrepolynomialsoperationalmatrixmethodforsolvingfractionalpartialdifferentialequationswithvariablecoefficients
AT lifengwang legendrepolynomialsoperationalmatrixmethodforsolvingfractionalpartialdifferentialequationswithvariablecoefficients
_version_ 1716789556629471232

Similar Items