An extended cubic B-spline collocation scheme for time fractional sub-diffusion equation

Tayyaba Akram; Muhammad Abbas; Ahmad Izani Ismail

doi:10.1063/1.5136449

An extended cubic B-spline collocation scheme for time fractional sub-diffusion equation

Tayyaba Akram^*
, Muhammad Abbas
, Ahmad Izani Ismail

^*Corresponding author for this work

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

17 Scopus citations

Abstract

In this paper, an extended cubic B-spline scheme is developed to solve the time fractional sub-diffusion equation. The time fractional derivative is represented using Caputo's formula and the discretization utilizes the θ-weighted scheme. The scheme is unconditionally stable and the convergence is shown to be of second order. The results of numerical experiments indicate the effectiveness of the proposed method.

Original language	English
Title of host publication	Proceedings of the International Conference on Mathematical Sciences and Technology 2018, MathTech 2018
Subtitle of host publication	Innovative Technologies for Mathematics and Mathematics for Technological Innovation
Editors	Yazariah Mohd Yatim, Syakila Ahmad, Mohd Tahir Ismail, Majid Khan Majahar Ali, Rosmanjawati Abdul Rahman, Hajar Sulaiman, Norshafira Ramli, Noor Atinah Ahmad, Farah Aini Abdullah
Publisher	American Institute of Physics Inc.
ISBN (Electronic)	9780735419315
DOIs	https://doi.org/10.1063/1.5136449
State	Published - 4 Dec 2019
Externally published	Yes
Event	1st International Conference on Mathematical Sciences and Technology 2018: Innovative Technologies for Mathematics and Mathematics for Technological Innovation, MathTech 2018 - Penang, Malaysia Duration: 10 Dec 2018 → 12 Dec 2018

Publication series

Name	AIP Conference Proceedings
Volume	2184
ISSN (Print)	0094-243X
ISSN (Electronic)	1551-7616

Conference

Conference	1st International Conference on Mathematical Sciences and Technology 2018: Innovative Technologies for Mathematics and Mathematics for Technological Innovation, MathTech 2018
Country/Territory	Malaysia
City	Penang
Period	10/12/18 → 12/12/18

Bibliographical note

Publisher Copyright:
© 2019 Author(s).

ASJC Scopus subject areas

General Physics and Astronomy

Access to Document

10.1063/1.5136449

Cite this

Akram, T., Abbas, M., & Ismail, A. I. (2019). An extended cubic B-spline collocation scheme for time fractional sub-diffusion equation. In Y. M. Yatim, S. Ahmad, M. T. Ismail, M. K. M. Ali, R. A. Rahman, H. Sulaiman, N. Ramli, N. A. Ahmad, & F. A. Abdullah (Eds.), Proceedings of the International Conference on Mathematical Sciences and Technology 2018, MathTech 2018: Innovative Technologies for Mathematics and Mathematics for Technological Innovation Article 060017 (AIP Conference Proceedings; Vol. 2184). American Institute of Physics Inc.. https://doi.org/10.1063/1.5136449

Akram, Tayyaba ; Abbas, Muhammad ; Ismail, Ahmad Izani. / An extended cubic B-spline collocation scheme for time fractional sub-diffusion equation. Proceedings of the International Conference on Mathematical Sciences and Technology 2018, MathTech 2018: Innovative Technologies for Mathematics and Mathematics for Technological Innovation. editor / Yazariah Mohd Yatim ; Syakila Ahmad ; Mohd Tahir Ismail ; Majid Khan Majahar Ali ; Rosmanjawati Abdul Rahman ; Hajar Sulaiman ; Norshafira Ramli ; Noor Atinah Ahmad ; Farah Aini Abdullah. American Institute of Physics Inc., 2019. (AIP Conference Proceedings).

@inproceedings{bc8cbe1515384cea98a5ee99c746c6c0,

title = "An extended cubic B-spline collocation scheme for time fractional sub-diffusion equation",

abstract = "In this paper, an extended cubic B-spline scheme is developed to solve the time fractional sub-diffusion equation. The time fractional derivative is represented using Caputo's formula and the discretization utilizes the θ-weighted scheme. The scheme is unconditionally stable and the convergence is shown to be of second order. The results of numerical experiments indicate the effectiveness of the proposed method.",

author = "Tayyaba Akram and Muhammad Abbas and Ismail, \{Ahmad Izani\}",

note = "Publisher Copyright: {\textcopyright} 2019 Author(s).; 1st International Conference on Mathematical Sciences and Technology 2018: Innovative Technologies for Mathematics and Mathematics for Technological Innovation, MathTech 2018 ; Conference date: 10-12-2018 Through 12-12-2018",

year = "2019",

month = dec,

day = "4",

doi = "10.1063/1.5136449",

language = "English",

series = "AIP Conference Proceedings",

publisher = "American Institute of Physics Inc.",

editor = "Yatim, \{Yazariah Mohd\} and Syakila Ahmad and Ismail, \{Mohd Tahir\} and Ali, \{Majid Khan Majahar\} and Rahman, \{Rosmanjawati Abdul\} and Hajar Sulaiman and Norshafira Ramli and Ahmad, \{Noor Atinah\} and Abdullah, \{Farah Aini\}",

booktitle = "Proceedings of the International Conference on Mathematical Sciences and Technology 2018, MathTech 2018",

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Akram, T, Abbas, M & Ismail, AI 2019, An extended cubic B-spline collocation scheme for time fractional sub-diffusion equation. in YM Yatim, S Ahmad, MT Ismail, MKM Ali, RA Rahman, H Sulaiman, N Ramli, NA Ahmad & FA Abdullah (eds), Proceedings of the International Conference on Mathematical Sciences and Technology 2018, MathTech 2018: Innovative Technologies for Mathematics and Mathematics for Technological Innovation., 060017, AIP Conference Proceedings, vol. 2184, American Institute of Physics Inc., 1st International Conference on Mathematical Sciences and Technology 2018: Innovative Technologies for Mathematics and Mathematics for Technological Innovation, MathTech 2018, Penang, Malaysia, 10/12/18. https://doi.org/10.1063/1.5136449

An extended cubic B-spline collocation scheme for time fractional sub-diffusion equation. / Akram, Tayyaba; Abbas, Muhammad; Ismail, Ahmad Izani.
Proceedings of the International Conference on Mathematical Sciences and Technology 2018, MathTech 2018: Innovative Technologies for Mathematics and Mathematics for Technological Innovation. ed. / Yazariah Mohd Yatim; Syakila Ahmad; Mohd Tahir Ismail; Majid Khan Majahar Ali; Rosmanjawati Abdul Rahman; Hajar Sulaiman; Norshafira Ramli; Noor Atinah Ahmad; Farah Aini Abdullah. American Institute of Physics Inc., 2019. 060017 (AIP Conference Proceedings; Vol. 2184).

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

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AU - Akram, Tayyaba

AU - Abbas, Muhammad

AU - Ismail, Ahmad Izani

PY - 2019/12/4

Y1 - 2019/12/4

N2 - In this paper, an extended cubic B-spline scheme is developed to solve the time fractional sub-diffusion equation. The time fractional derivative is represented using Caputo's formula and the discretization utilizes the θ-weighted scheme. The scheme is unconditionally stable and the convergence is shown to be of second order. The results of numerical experiments indicate the effectiveness of the proposed method.

AB - In this paper, an extended cubic B-spline scheme is developed to solve the time fractional sub-diffusion equation. The time fractional derivative is represented using Caputo's formula and the discretization utilizes the θ-weighted scheme. The scheme is unconditionally stable and the convergence is shown to be of second order. The results of numerical experiments indicate the effectiveness of the proposed method.

UR - https://www.scopus.com/pages/publications/85076725094

U2 - 10.1063/1.5136449

DO - 10.1063/1.5136449

M3 - Conference contribution

AN - SCOPUS:85076725094

T3 - AIP Conference Proceedings

BT - Proceedings of the International Conference on Mathematical Sciences and Technology 2018, MathTech 2018

A2 - Yatim, Yazariah Mohd

A2 - Ahmad, Syakila

A2 - Ismail, Mohd Tahir

A2 - Ali, Majid Khan Majahar

A2 - Rahman, Rosmanjawati Abdul

A2 - Sulaiman, Hajar

A2 - Ramli, Norshafira

A2 - Ahmad, Noor Atinah

A2 - Abdullah, Farah Aini

PB - American Institute of Physics Inc.

T2 - 1st International Conference on Mathematical Sciences and Technology 2018: Innovative Technologies for Mathematics and Mathematics for Technological Innovation, MathTech 2018

Y2 - 10 December 2018 through 12 December 2018

ER -

Akram T, Abbas M, Ismail AI. An extended cubic B-spline collocation scheme for time fractional sub-diffusion equation. In Yatim YM, Ahmad S, Ismail MT, Ali MKM, Rahman RA, Sulaiman H, Ramli N, Ahmad NA, Abdullah FA, editors, Proceedings of the International Conference on Mathematical Sciences and Technology 2018, MathTech 2018: Innovative Technologies for Mathematics and Mathematics for Technological Innovation. American Institute of Physics Inc. 2019. 060017. (AIP Conference Proceedings). doi: 10.1063/1.5136449

An extended cubic B-spline collocation scheme for time fractional sub-diffusion equation

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