Legendre Wavelets Direct Method for the Numerical Solution of Time-Fractional Order Telegraph Equations

被引：18

作者：

Xu, Xiaoyong ^{[1
,2
]}

Xu, Da ^{[1
]}

机构：

[1] Hunan Normal Univ, Coll Math & Comp Sci, Changsha 410006, Hunan, Peoples R China

[2] East China Univ Technol, Sch Sci, Nanchang 330013, Jiangxi, Peoples R China

来源：

MEDITERRANEAN JOURNAL OF MATHEMATICS | 2018年 / 15卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Legendre wavelets; time-fractional order telegraph equation; Riemann-Liouville integral; shifted Legendre polynomials; collocation method; PARTIAL-DIFFERENTIAL-EQUATIONS; COLLOCATION METHOD;

D O I：

10.1007/s00009-018-1074-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, a Legendre wavelet collocation method for solving a class of time-fractional order telegraph equation defined by Caputo sense is discussed. Fractional integral formula of a single Legendre wavelet in the Riemann-Liouville sense is derived by means of shifted Legendre polynomials. The main characteristic behind this approach is that it reduces equations to those of solving a system of algebraic equations which greatly simplifies the problem. The convergence analysis and error analysis of the proposed method are investigated. Several examples are presented to show the applicability and accuracy of the proposed method.

引用

页数：33

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