Reaction Coefficient Identification Problem for a Time-Fractional Diffusion Equation

Ibrahim O. Sarumi

doi:10.1109/ICFDA58234.2023.10153164

Reaction Coefficient Identification Problem for a Time-Fractional Diffusion Equation

Ibrahim O. Sarumi^*

^*Corresponding author for this work

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

1 Scopus citations

Abstract

In this paper, we examine the recovery of a space-dependent reaction coefficient for a one-dimensional linear reaction-diffusion equation. The diffusion problem is coupled with a reading of the solution profile at a specified time. Our recovery approach is based on the pseudo-spectral method which is used to formulate a system of time-fractional differential equations involving Fourier coefficients of the solution as well as those of the reaction-coefficient. The resulting differential system is discretized by an exponential time differencing type scheme to obtain a linear algebraic system whose solution approximates the Fourier coefficients of the reaction coefficient. Numerical experiments are presented to illustrate the performance of the proposed method.

Original language	English
Title of host publication	2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023
Publisher	Institute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)	9798350321685
DOIs	https://doi.org/10.1109/ICFDA58234.2023.10153164
State	Published - 2023
Event	2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023 - Ajman, United Arab Emirates Duration: 14 Mar 2023 → 16 Mar 2023

Publication series

Name	2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023

Conference

Conference	2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023
Country/Territory	United Arab Emirates
City	Ajman
Period	14/03/23 → 16/03/23

Bibliographical note

Publisher Copyright:
© 2023 IEEE.

Keywords

Coefficient identification
Coefficient inverse problem
Pseudo-spectral method
Time-fractional diffusion

ASJC Scopus subject areas

Analysis
Applied Mathematics
Mathematical Physics
Numerical Analysis

Access to Document

10.1109/ICFDA58234.2023.10153164

Cite this

Sarumi, I. O. (2023). Reaction Coefficient Identification Problem for a Time-Fractional Diffusion Equation. In 2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023 (2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ICFDA58234.2023.10153164

@inproceedings{697fce085eb7456da5cb395901dc9bf7,

title = "Reaction Coefficient Identification Problem for a Time-Fractional Diffusion Equation",

abstract = "In this paper, we examine the recovery of a space-dependent reaction coefficient for a one-dimensional linear reaction-diffusion equation. The diffusion problem is coupled with a reading of the solution profile at a specified time. Our recovery approach is based on the pseudo-spectral method which is used to formulate a system of time-fractional differential equations involving Fourier coefficients of the solution as well as those of the reaction-coefficient. The resulting differential system is discretized by an exponential time differencing type scheme to obtain a linear algebraic system whose solution approximates the Fourier coefficients of the reaction coefficient. Numerical experiments are presented to illustrate the performance of the proposed method.",

keywords = "Coefficient identification, Coefficient inverse problem, Pseudo-spectral method, Time-fractional diffusion",

author = "Sarumi, \{Ibrahim O.\}",

note = "Publisher Copyright: {\textcopyright} 2023 IEEE.; 2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023 ; Conference date: 14-03-2023 Through 16-03-2023",

year = "2023",

doi = "10.1109/ICFDA58234.2023.10153164",

language = "English",

series = "2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

booktitle = "2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023",

address = "United States",

}

Sarumi, IO 2023, Reaction Coefficient Identification Problem for a Time-Fractional Diffusion Equation. in 2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023. 2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023, Institute of Electrical and Electronics Engineers Inc., 2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023, Ajman, United Arab Emirates, 14/03/23. https://doi.org/10.1109/ICFDA58234.2023.10153164

Reaction Coefficient Identification Problem for a Time-Fractional Diffusion Equation. / Sarumi, Ibrahim O.
2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023. Institute of Electrical and Electronics Engineers Inc., 2023. (2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023).

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

TY - GEN

T1 - Reaction Coefficient Identification Problem for a Time-Fractional Diffusion Equation

AU - Sarumi, Ibrahim O.

PY - 2023

Y1 - 2023

N2 - In this paper, we examine the recovery of a space-dependent reaction coefficient for a one-dimensional linear reaction-diffusion equation. The diffusion problem is coupled with a reading of the solution profile at a specified time. Our recovery approach is based on the pseudo-spectral method which is used to formulate a system of time-fractional differential equations involving Fourier coefficients of the solution as well as those of the reaction-coefficient. The resulting differential system is discretized by an exponential time differencing type scheme to obtain a linear algebraic system whose solution approximates the Fourier coefficients of the reaction coefficient. Numerical experiments are presented to illustrate the performance of the proposed method.

AB - In this paper, we examine the recovery of a space-dependent reaction coefficient for a one-dimensional linear reaction-diffusion equation. The diffusion problem is coupled with a reading of the solution profile at a specified time. Our recovery approach is based on the pseudo-spectral method which is used to formulate a system of time-fractional differential equations involving Fourier coefficients of the solution as well as those of the reaction-coefficient. The resulting differential system is discretized by an exponential time differencing type scheme to obtain a linear algebraic system whose solution approximates the Fourier coefficients of the reaction coefficient. Numerical experiments are presented to illustrate the performance of the proposed method.

KW - Coefficient identification

KW - Coefficient inverse problem

KW - Pseudo-spectral method

KW - Time-fractional diffusion

UR - https://www.scopus.com/pages/publications/85164537757

U2 - 10.1109/ICFDA58234.2023.10153164

DO - 10.1109/ICFDA58234.2023.10153164

M3 - Conference contribution

AN - SCOPUS:85164537757

T3 - 2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023

BT - 2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023

Y2 - 14 March 2023 through 16 March 2023

ER -

Sarumi IO. Reaction Coefficient Identification Problem for a Time-Fractional Diffusion Equation. In 2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023. Institute of Electrical and Electronics Engineers Inc. 2023. (2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023). doi: 10.1109/ICFDA58234.2023.10153164

Reaction Coefficient Identification Problem for a Time-Fractional Diffusion Equation

Abstract

Publication series

Conference

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Fingerprint

Cite this