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Calcolo
Erschienen in: Calcolo 1/2016

01.03.2016

A numerical technique based on the shifted Legendre polynomials for solving the time-fractional coupled KdV equations

verfasst von: A. H. Bhrawy, E. H. Doha, S. S. Ezz-Eldien, M. A. Abdelkawy

Erschienen in: Calcolo | Ausgabe 1/2016

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Abstract

The time-fractional coupled Korteweg–de Vries (KdV) system is a generalization of the classical coupled KdV system and obtained by replacing the first order time derivatives by fractional derivatives of orders \(\nu _1\) and \(\nu _2\), \((0<\nu _1,\nu _2\le 1).\) In this paper, an accurate and robust numerical technique is proposed for solving the time-fractional coupled KdV equations. The shifted Legendre polynomials are introduced as basis functions of the collocation spectral method together with the operational matrix of fractional derivatives (described in the Caputo sense) in order to reduce the time-fractional coupled KdV equations into a problem consisting of a system of algebraic equations that greatly simplifies the problem. In order to test the efficiency and validity of the proposed numerical technique, we apply it to solve two numerical examples.
Nächster Artikel On long time integration of the heat equation

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Metadaten
Titel
A numerical technique based on the shifted Legendre polynomials for solving the time-fractional coupled KdV equations
verfasst von
A. H. Bhrawy
E. H. Doha
S. S. Ezz-Eldien
M. A. Abdelkawy
Publikationsdatum
01.03.2016
Verlag
Springer Milan
Erschienen in
Calcolo / Ausgabe 1/2016
Print ISSN: 0008-0624
Elektronische ISSN: 1126-5434
DOI
https://doi.org/10.1007/s10092-014-0132-x

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