An Effective Numerical Technique Based on the Tau Method for the Eigenvalue Problems

Maryam Attary; Praveen Agarwal

doi:10.1007/978-981-15-0430-3_12

An Effective Numerical Technique Based on the Tau Method for the Eigenvalue Problems

Maryam Attary
, Praveen Agarwal

Islamic Azad University
International College of Engineering
Harish Chandra Research Institute
International Center for Basic and Applied Sciences

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

We consider the (presumably new) effective numerical scheme based on the Legendre polynomials for an approximate solution of eigenvalue problems. First, a new operational matrix, which can be represented by a sparse matrix defined by using the Tau method and orthogonal functions. Sparse data is by nature more compressed and thus requires significantly less storage. A comparison of the results for some examples reveals that the presented method is convenient and effective, also we consider the problem of column buckling to show the validity of the proposed method.

Original language	English
Title of host publication	Fractional Calculus - ICFDA 2018
Editors	Praveen Agarwal, Praveen Agarwal, Praveen Agarwal, Dumitru Baleanu, YangQuan Chen, Shaher Momani, José António Tenreiro Machado
Publisher	Springer
Pages	215-226
Number of pages	12
ISBN (Print)	9789811504297
DOIs	https://doi.org/10.1007/978-981-15-0430-3_12
State	Published - 2019
Externally published	Yes
Event	International Conference on Fractional Differentiation and its Applications, ICFDA 2018 - Amman, Jordan Duration: 16 Jul 2018 → 18 Jul 2018

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	303
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	International Conference on Fractional Differentiation and its Applications, ICFDA 2018
Country/Territory	Jordan
City	Amman
Period	16/07/18 → 18/07/18

Keywords

Eigenvalue problems
Legendre polynomials
Numerical treatment

Access to Document

10.1007/978-981-15-0430-3_12

Cite this

Attary, M., & Agarwal, P. (2019). An Effective Numerical Technique Based on the Tau Method for the Eigenvalue Problems. In P. Agarwal, P. Agarwal, P. Agarwal, D. Baleanu, Y. Chen, S. Momani, & J. A. T. Machado (Eds.), Fractional Calculus - ICFDA 2018 (pp. 215-226). (Springer Proceedings in Mathematics and Statistics; Vol. 303). Springer. https://doi.org/10.1007/978-981-15-0430-3_12

Attary, Maryam ; Agarwal, Praveen. / An Effective Numerical Technique Based on the Tau Method for the Eigenvalue Problems. Fractional Calculus - ICFDA 2018. editor / Praveen Agarwal ; Praveen Agarwal ; Praveen Agarwal ; Dumitru Baleanu ; YangQuan Chen ; Shaher Momani ; José António Tenreiro Machado. Springer, 2019. pp. 215-226 (Springer Proceedings in Mathematics and Statistics).

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title = "An Effective Numerical Technique Based on the Tau Method for the Eigenvalue Problems",

abstract = "We consider the (presumably new) effective numerical scheme based on the Legendre polynomials for an approximate solution of eigenvalue problems. First, a new operational matrix, which can be represented by a sparse matrix defined by using the Tau method and orthogonal functions. Sparse data is by nature more compressed and thus requires significantly less storage. A comparison of the results for some examples reveals that the presented method is convenient and effective, also we consider the problem of column buckling to show the validity of the proposed method.",

keywords = "Eigenvalue problems, Legendre polynomials, Numerical treatment",

author = "Maryam Attary and Praveen Agarwal",

note = "Publisher Copyright: {\textcopyright} 2019, Springer Nature Singapore Pte Ltd.; International Conference on Fractional Differentiation and its Applications, ICFDA 2018 ; Conference date: 16-07-2018 Through 18-07-2018",

year = "2019",

doi = "10.1007/978-981-15-0430-3\_12",

language = "English",

isbn = "9789811504297",

series = "Springer Proceedings in Mathematics and Statistics",

publisher = "Springer",

pages = "215--226",

editor = "Praveen Agarwal and Praveen Agarwal and Praveen Agarwal and Dumitru Baleanu and YangQuan Chen and Shaher Momani and Machado, \{Jos{\'e} Ant{\'o}nio Tenreiro\}",

booktitle = "Fractional Calculus - ICFDA 2018",

address = "Germany",

}

Attary, M & Agarwal, P 2019, An Effective Numerical Technique Based on the Tau Method for the Eigenvalue Problems. in P Agarwal, P Agarwal, P Agarwal, D Baleanu, Y Chen, S Momani & JAT Machado (eds), Fractional Calculus - ICFDA 2018. Springer Proceedings in Mathematics and Statistics, vol. 303, Springer, pp. 215-226, International Conference on Fractional Differentiation and its Applications, ICFDA 2018, Amman, Jordan, 16/07/18. https://doi.org/10.1007/978-981-15-0430-3_12

An Effective Numerical Technique Based on the Tau Method for the Eigenvalue Problems. / Attary, Maryam; Agarwal, Praveen.
Fractional Calculus - ICFDA 2018. ed. / Praveen Agarwal; Praveen Agarwal; Praveen Agarwal; Dumitru Baleanu; YangQuan Chen; Shaher Momani; José António Tenreiro Machado. Springer, 2019. p. 215-226 (Springer Proceedings in Mathematics and Statistics; Vol. 303).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - An Effective Numerical Technique Based on the Tau Method for the Eigenvalue Problems

AU - Attary, Maryam

AU - Agarwal, Praveen

PY - 2019

Y1 - 2019

N2 - We consider the (presumably new) effective numerical scheme based on the Legendre polynomials for an approximate solution of eigenvalue problems. First, a new operational matrix, which can be represented by a sparse matrix defined by using the Tau method and orthogonal functions. Sparse data is by nature more compressed and thus requires significantly less storage. A comparison of the results for some examples reveals that the presented method is convenient and effective, also we consider the problem of column buckling to show the validity of the proposed method.

AB - We consider the (presumably new) effective numerical scheme based on the Legendre polynomials for an approximate solution of eigenvalue problems. First, a new operational matrix, which can be represented by a sparse matrix defined by using the Tau method and orthogonal functions. Sparse data is by nature more compressed and thus requires significantly less storage. A comparison of the results for some examples reveals that the presented method is convenient and effective, also we consider the problem of column buckling to show the validity of the proposed method.

KW - Eigenvalue problems

KW - Legendre polynomials

KW - Numerical treatment

UR - https://www.scopus.com/pages/publications/85076754761

U2 - 10.1007/978-981-15-0430-3_12

DO - 10.1007/978-981-15-0430-3_12

M3 - Conference contribution

AN - SCOPUS:85076754761

SN - 9789811504297

T3 - Springer Proceedings in Mathematics and Statistics

SP - 215

EP - 226

BT - Fractional Calculus - ICFDA 2018

A2 - Agarwal, Praveen

A2 - Baleanu, Dumitru

A2 - Chen, YangQuan

A2 - Momani, Shaher

A2 - Machado, José António Tenreiro

PB - Springer

T2 - International Conference on Fractional Differentiation and its Applications, ICFDA 2018

Y2 - 16 July 2018 through 18 July 2018

ER -

An Effective Numerical Technique Based on the Tau Method for the Eigenvalue Problems

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