An innovative harmonic numbers operational matrix method for solving initial value problems

被引：0
|
作者：
Anna Napoli
W. M. Abd-Elhameed
机构：
[1] University of Calabria,Department of Mathematics and Informatics
[2] University of Jeddah,Department of Mathematics, Faculty of Science
[3] Cairo University,Department of Mathematics, Faculty of Science
来源：
Calcolo | 2017年 / 54卷
关键词：
Initial value problems; Spectral methods; Legendre polynomials; Harmonic numbers; 65L05; 42C15;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper a novel operational matrix of derivatives of certain basis of Legendre polynomials is established. We show that this matrix is expressed in terms of the harmonic numbers. Moreover, it is utilized along with the collocation method for handling initial value problems of any order. The convergence and the error analysis of the proposed expansion are carefully investigated. Numerical examples are exhibited to confirm the reliability and the high efficiency of the proposed method.
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页码：57 / 76
页数：19
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