Numerical solutions of fractional partial differential equations by using Legendre wavelets

Hao Song; Mingxu Yi; Jun Huang; Yalin Pan

Numerical solutions of fractional partial differential equations by using Legendre wavelets

Hao Song
, Mingxu Yi^*
, Jun Huang
, Yalin Pan

^*此作品的通讯作者

航空科学与工程学院

Beihang University

科研成果: 期刊稿件 › 文章 › 同行评审

14 引用（Scopus）

摘要

A numerical method based on Legendre wavelets is proposed for fractional partial differential equations. Legendre wavelets operational matrices of fractional order integration and fractional order differentiation are derived. By using these matrices, each term of the problem was converted into matrix form. Lastly, the equation was transformed into a Sylvester equation. The error estimation of the Legendre wavelets method is given in Theorem 5.1. Three numerical examples are shown to demonstrate the validity and applicability of the method.

源语言	英语
页（从-至）	358-364
页数	7
期刊	Engineering Letters
卷	24
期	3
出版状态	已出版 - 2016

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引用此

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title = "Numerical solutions of fractional partial differential equations by using Legendre wavelets",

abstract = "A numerical method based on Legendre wavelets is proposed for fractional partial differential equations. Legendre wavelets operational matrices of fractional order integration and fractional order differentiation are derived. By using these matrices, each term of the problem was converted into matrix form. Lastly, the equation was transformed into a Sylvester equation. The error estimation of the Legendre wavelets method is given in Theorem 5.1. Three numerical examples are shown to demonstrate the validity and applicability of the method.",

keywords = "Error analysis, Fractional partial differential equation, Legendre wavelets, Operational matrix, Sylvester equation",

author = "Hao Song and Mingxu Yi and Jun Huang and Yalin Pan",

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AU - Song, Hao

AU - Yi, Mingxu

AU - Huang, Jun

AU - Pan, Yalin

PY - 2016

Y1 - 2016

N2 - A numerical method based on Legendre wavelets is proposed for fractional partial differential equations. Legendre wavelets operational matrices of fractional order integration and fractional order differentiation are derived. By using these matrices, each term of the problem was converted into matrix form. Lastly, the equation was transformed into a Sylvester equation. The error estimation of the Legendre wavelets method is given in Theorem 5.1. Three numerical examples are shown to demonstrate the validity and applicability of the method.

AB - A numerical method based on Legendre wavelets is proposed for fractional partial differential equations. Legendre wavelets operational matrices of fractional order integration and fractional order differentiation are derived. By using these matrices, each term of the problem was converted into matrix form. Lastly, the equation was transformed into a Sylvester equation. The error estimation of the Legendre wavelets method is given in Theorem 5.1. Three numerical examples are shown to demonstrate the validity and applicability of the method.

KW - Error analysis

KW - Fractional partial differential equation

KW - Legendre wavelets

KW - Operational matrix

KW - Sylvester equation

UR - https://www.scopus.com/pages/publications/84984820536

M3 - 文章

AN - SCOPUS:84984820536

SN - 1816-093X

VL - 24

SP - 358

EP - 364

JO - Engineering Letters

JF - Engineering Letters

IS - 3

ER -

Numerical solutions of fractional partial differential equations by using Legendre wavelets

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