An hp-version Legendre spectral collocation method for multi-order fractional differential equations

被引：6

作者：

Guo, Yuling ^{[1
]}

Wang, Zhongqing ^{[1
]}

机构：

[1] Univ Shanghai Sci & Technol, Coll Sci, Shanghai 200093, Peoples R China

来源：

ADVANCES IN COMPUTATIONAL MATHEMATICS | 2021年 / 47卷 / 03期

基金：

中国国家自然科学基金; 中国博士后科学基金;

关键词：

Multi-order fractional differential equations; Legendre spectral collocation method; hp-version error bounds; APPROXIMATION;

D O I：

10.1007/s10444-021-09858-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the multi-order fractional differential equation and recast it into an integral equation. Based on the integral equation, we develop an hp-version Legendre spectral collocation method and the integral terms with the weakly singular kernels are calculated precisely according to the properties of Legendre and Jacobi polynomials. The hp-version error bounds under the L-2-norm and the L-infinity-norm are derived rigorously. Numerical experiments are included to illustrate the efficiency of the proposed method and the rationality of the theoretical results.

引用

页数：27

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