A note on a stable algorithm for computing the fractional integrals of orthogonal polynomials

被引：4

作者：

Amodio, Pierluigi ^{[1
]}

Brugnano, Luigi ^{[2
]}

Iavernaro, Felice ^{[1
]}

机构：

[1] Univ Bari, Dipartimento Matemat, Bari, Italy

[2] Univ Firenze, Dipartimento Matemat & Informat U Dini, Florence, Italy

来源：

APPLIED MATHEMATICS LETTERS | 2022年 / 134卷

关键词：

Fractional differential equations; Fractional integrals; Orthogonal polynomials; Legendre polynomials; Chebyshev polynomials;

D O I：

10.1016/j.aml.2022.108338

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this note we provide an algorithm for computing the fractional integrals of orthogonal polynomials, which is more stable than the one based on the expansion of the polynomials w.r.t. the canonical basis. This algorithm is aimed at solving corresponding fractional differential equations. A few numerical illustrations are reported. (C) 2022 Elsevier Ltd. All rights reserved.

引用

页数：8

共 50 条

[11] A NOTE ON MULTILINEAR FRACTIONAL INTEGRALS
Takeshi Iida
Yasuo Komori-Furuya
Enji Sato
AnalysisinTheoryandApplications, 2010, 26 (04) : 301 - 307
[12] Computing polynomials orthogonal with respect to densely oscillating and exponentially decaying weight functions and related integrals
Gautschi, W
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2005, 184 (02) : 493 - 504
[13] BETA-INTEGRALS AND THE ASSOCIATED ORTHOGONAL POLYNOMIALS
ASKEY, R
LECTURE NOTES IN MATHEMATICS, 1989, 1395 : 84 - 121
[14] A note on integer polynomials with small integrals
Bazzanella, D.
ACTA MATHEMATICA HUNGARICA, 2013, 141 (04) : 320 - 328
[15] A note on integer polynomials with small integrals
Danilo Bazzanella
Acta Mathematica Hungarica, 2013, 141 : 320 - 328
[16] COMPUTING ORTHOGONAL POLYNOMIALS IN SOBOLEV SPACES
GAUTSCHI, W
ZHANG, MD
NUMERISCHE MATHEMATIK, 1995, 71 (02) : 159 - 183
[17] Some orthogonal polynomials on the finite interval and Gaussian quadrature rules for fractional Riemann-Liouville integrals
Milovanovic, Gradimir V.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2021, 44 (01) : 493 - 516
[18] A NOTE ON THE ZERO DISTRIBUTION OF ORTHOGONAL POLYNOMIALS
MERCER, AM
JOURNAL OF APPROXIMATION THEORY, 1991, 64 (02) : 238 - 242
[19] A NOTE ON RECURSIVELY DEFINED ORTHOGONAL POLYNOMIALS
MAKI, DP
PACIFIC JOURNAL OF MATHEMATICS, 1969, 28 (03) : 611 - &
[20] A NOTE ON PROPERTY (T) OF ORTHOGONAL POLYNOMIALS
LASSER, R
ROSLER, M
ARCHIV DER MATHEMATIK, 1993, 60 (05) : 459 - 463

← 1 2 3 4 5 →