Chebyshev spectral approximation for diffusion equations with distributed order in time

Maria Luísa Morgado; Magda Rebelo

doi:10.1007/978-3-319-32857-7_24

Chebyshev spectral approximation for diffusion equations with distributed order in time

Maria Luísa Morgado, Magda Rebelo

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

Abstract

In this work we provide a numerical method for the diffusion equation with distributed order in time. The basic idea is to expand the unknown function in Chebyshev polynomials for the time variable t and reduce the problem to the solution of a system of algebraic equations, which may then be solved by any standard numerical technique. We apply the method to the forward and backward problems. Some numerical experiments are provided in order to show the performance and accuracy of the proposed method.

Original language	English
Title of host publication	Differential and Difference Equations with Applications - ICDDEA, Selected Contributions
Publisher	Springer New York LLC
Pages	255-263
Number of pages	9
Volume	164
ISBN (Print)	9783319328553
DOIs	https://doi.org/10.1007/978-3-319-32857-7_24
Publication status	Published - 2016
Event	International Conference on Differential and Difference Equations with Applications, ICDDEA 2015 - Amadora, Portugal Duration: 18 May 2015 → 22 May 2015

Conference

Conference	International Conference on Differential and Difference Equations with Applications, ICDDEA 2015
Country/Territory	Portugal
City	Amadora
Period	18/05/15 → 22/05/15

Keywords

Caputo derivative
Chebyshev polynomials
Diffusion equation
Distributed order equation
Fractional differential equation

Access to Document

10.1007/978-3-319-32857-7_24

Cite this

@inproceedings{c3a44db857ed491ebbf8affcfcf14ec4,

title = "Chebyshev spectral approximation for diffusion equations with distributed order in time",

abstract = "In this work we provide a numerical method for the diffusion equation with distributed order in time. The basic idea is to expand the unknown function in Chebyshev polynomials for the time variable t and reduce the problem to the solution of a system of algebraic equations, which may then be solved by any standard numerical technique. We apply the method to the forward and backward problems. Some numerical experiments are provided in order to show the performance and accuracy of the proposed method.",

keywords = "Caputo derivative, Chebyshev polynomials, Diffusion equation, Distributed order equation, Fractional differential equation",

author = "Morgado, {Maria Lu{\'i}sa} and Magda Rebelo",

note = "sem pdf Portuguese Foundation for Science and Technology (FCT) - UID/MAT/00013/2013 ; UID/MAT/00297/2013 ; International Conference on Differential and Difference Equations with Applications, ICDDEA 2015 ; Conference date: 18-05-2015 Through 22-05-2015",

year = "2016",

doi = "10.1007/978-3-319-32857-7_24",

language = "English",

isbn = "9783319328553",

volume = "164",

pages = "255--263",

booktitle = "Differential and Difference Equations with Applications - ICDDEA, Selected Contributions",

publisher = "Springer New York LLC",

}

Morgado, ML & Rebelo, M 2016, Chebyshev spectral approximation for diffusion equations with distributed order in time. in Differential and Difference Equations with Applications - ICDDEA, Selected Contributions. vol. 164, Springer New York LLC, pp. 255-263, International Conference on Differential and Difference Equations with Applications, ICDDEA 2015, Amadora, Portugal, 18/05/15. https://doi.org/10.1007/978-3-319-32857-7_24

Chebyshev spectral approximation for diffusion equations with distributed order in time. / Morgado, Maria Luísa; Rebelo, Magda.
Differential and Difference Equations with Applications - ICDDEA, Selected Contributions. Vol. 164 Springer New York LLC, 2016. p. 255-263.

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

TY - GEN

T1 - Chebyshev spectral approximation for diffusion equations with distributed order in time

AU - Morgado, Maria Luísa

AU - Rebelo, Magda

N1 - sem pdf Portuguese Foundation for Science and Technology (FCT) - UID/MAT/00013/2013 ; UID/MAT/00297/2013

PY - 2016

Y1 - 2016

N2 - In this work we provide a numerical method for the diffusion equation with distributed order in time. The basic idea is to expand the unknown function in Chebyshev polynomials for the time variable t and reduce the problem to the solution of a system of algebraic equations, which may then be solved by any standard numerical technique. We apply the method to the forward and backward problems. Some numerical experiments are provided in order to show the performance and accuracy of the proposed method.

AB - In this work we provide a numerical method for the diffusion equation with distributed order in time. The basic idea is to expand the unknown function in Chebyshev polynomials for the time variable t and reduce the problem to the solution of a system of algebraic equations, which may then be solved by any standard numerical technique. We apply the method to the forward and backward problems. Some numerical experiments are provided in order to show the performance and accuracy of the proposed method.

KW - Caputo derivative

KW - Chebyshev polynomials

KW - Diffusion equation

KW - Distributed order equation

KW - Fractional differential equation

UR - http://www.scopus.com/inward/record.url?scp=84988728218&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-32857-7_24

DO - 10.1007/978-3-319-32857-7_24

M3 - Conference contribution

AN - SCOPUS:84988728218

SN - 9783319328553

VL - 164

SP - 255

EP - 263

BT - Differential and Difference Equations with Applications - ICDDEA, Selected Contributions

PB - Springer New York LLC

T2 - International Conference on Differential and Difference Equations with Applications, ICDDEA 2015

Y2 - 18 May 2015 through 22 May 2015

ER -

Chebyshev spectral approximation for diffusion equations with distributed order in time

Abstract

Conference

Keywords

Access to Document

Other files and links

Fingerprint

Cite this