Fractional-order Legendre-collocation method for solving fractional initial value problems

Qasem M. Al-Mdallal; Ahmed S. Abu Omer

doi:10.1016/j.amc.2017.10.012

Fractional-order Legendre-collocation method for solving fractional initial value problems

Qasem M. Al-Mdallal, Ahmed S. Abu Omer

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

42 Citations (Scopus)

Abstract

In this paper, we present a numerical algorithm for solving second-order fractional initial value problems. This numerical algorithm is based on a fractional Legendre-collocation spectral method. The governing fractional differential equation is converted into a nonlinear system of algebraic equations. The error analysis of the proposed numerical algorithm is presented. Comparisons with other numerical methods shows that the proposed algorithm is more accurate and simpler to implement. Several examples are discussed to illustrate the efficiency and accuracy of the present scheme.

Original language	English
Pages (from-to)	74-84
Number of pages	11
Journal	Applied Mathematics and Computation
Volume	321
DOIs	https://doi.org/10.1016/j.amc.2017.10.012
Publication status	Published - Mar 15 2018

Keywords

Caputo derivative
Collocation method
Fractional Legendre functions
Spectral methods

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/j.amc.2017.10.012

Cite this

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title = "Fractional-order Legendre-collocation method for solving fractional initial value problems",

abstract = "In this paper, we present a numerical algorithm for solving second-order fractional initial value problems. This numerical algorithm is based on a fractional Legendre-collocation spectral method. The governing fractional differential equation is converted into a nonlinear system of algebraic equations. The error analysis of the proposed numerical algorithm is presented. Comparisons with other numerical methods shows that the proposed algorithm is more accurate and simpler to implement. Several examples are discussed to illustrate the efficiency and accuracy of the present scheme.",

keywords = "Caputo derivative, Collocation method, Fractional Legendre functions, Spectral methods",

author = "Al-Mdallal, {Qasem M.} and {Abu Omer}, {Ahmed S.}",

note = "Funding Information: The authors would like to express their appreciation for the valuable comments of the reviewers. The authors also would like to express their sincere appreciation to the United Arab Emirates University , Al Ain, UAE for providing the financial support with the Grants 31S212-UPAR (9) 2015 and 31S240-UPAR (2) 2016. Publisher Copyright: {\textcopyright} 2017 Elsevier Inc.",

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doi = "10.1016/j.amc.2017.10.012",

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T1 - Fractional-order Legendre-collocation method for solving fractional initial value problems

AU - Al-Mdallal, Qasem M.

AU - Abu Omer, Ahmed S.

N1 - Funding Information: The authors would like to express their appreciation for the valuable comments of the reviewers. The authors also would like to express their sincere appreciation to the United Arab Emirates University , Al Ain, UAE for providing the financial support with the Grants 31S212-UPAR (9) 2015 and 31S240-UPAR (2) 2016. Publisher Copyright: © 2017 Elsevier Inc.

PY - 2018/3/15

Y1 - 2018/3/15

N2 - In this paper, we present a numerical algorithm for solving second-order fractional initial value problems. This numerical algorithm is based on a fractional Legendre-collocation spectral method. The governing fractional differential equation is converted into a nonlinear system of algebraic equations. The error analysis of the proposed numerical algorithm is presented. Comparisons with other numerical methods shows that the proposed algorithm is more accurate and simpler to implement. Several examples are discussed to illustrate the efficiency and accuracy of the present scheme.

AB - In this paper, we present a numerical algorithm for solving second-order fractional initial value problems. This numerical algorithm is based on a fractional Legendre-collocation spectral method. The governing fractional differential equation is converted into a nonlinear system of algebraic equations. The error analysis of the proposed numerical algorithm is presented. Comparisons with other numerical methods shows that the proposed algorithm is more accurate and simpler to implement. Several examples are discussed to illustrate the efficiency and accuracy of the present scheme.

KW - Caputo derivative

KW - Collocation method

KW - Fractional Legendre functions

KW - Spectral methods

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EP - 84

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

ER -

Fractional-order Legendre-collocation method for solving fractional initial value problems

Abstract

Keywords

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