AN EFFICIENT NUMERICAL METHOD BASED ON CUBIC B-SPLINE FOR TIME DEPENDENT PROBLEM WITH SMALL PARAMETER

Kelthoum Lina Redouane; Nouria Arar; Qasem Al-Mdallal

doi:10.30546/2409-4994.48.2022.131152

AN EFFICIENT NUMERICAL METHOD BASED ON CUBIC B-SPLINE FOR TIME DEPENDENT PROBLEM WITH SMALL PARAMETER

Kelthoum Lina Redouane, Nouria Arar, Qasem Al-Mdallal

Department of Mathematical Sciences

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

1 Citation (Scopus)

Abstract

This work is devoted to the development of a Galerkin-type approximation of the solution of parabolic reaction-diffusion problems, utilizing cubic B-Spline functions and a finite difference scheme. An error estimate for the semi discrete weak Galerkin scheme is established. A Von Neumann stability study of the proposed fully discrete Crank Nicolson scheme is also performed. In addition, examples are used to validate the proposed approximation. The numerical results produced demonstrate the procedure’s efficacy and are in good agreement with the exact solution.

Original language	English
Pages (from-to)	131-152
Number of pages	22
Journal	Proceedings of the Institute of Mathematics and Mechanics
Volume	48
Issue number	Special Issue
DOIs	https://doi.org/10.30546/2409-4994.48.2022.131152
Publication status	Published - 2022

Keywords

Cubic B-splines
Finite Difference Scheme
Finite differences
Galerkin method
Parabolic problem

ASJC Scopus subject areas

Mathematics(all)

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10.30546/2409-4994.48.2022.131152

Cite this

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title = "AN EFFICIENT NUMERICAL METHOD BASED ON CUBIC B-SPLINE FOR TIME DEPENDENT PROBLEM WITH SMALL PARAMETER",

abstract = "This work is devoted to the development of a Galerkin-type approximation of the solution of parabolic reaction-diffusion problems, utilizing cubic B-Spline functions and a finite difference scheme. An error estimate for the semi discrete weak Galerkin scheme is established. A Von Neumann stability study of the proposed fully discrete Crank Nicolson scheme is also performed. In addition, examples are used to validate the proposed approximation. The numerical results produced demonstrate the procedure{\textquoteright}s efficacy and are in good agreement with the exact solution.",

keywords = "Cubic B-splines, Finite Difference Scheme, Finite differences, Galerkin method, Parabolic problem",

author = "Redouane, {Kelthoum Lina} and Nouria Arar and Qasem Al-Mdallal",

note = "Funding Information: K.L. Redouane and N. Arar acknowledge support from Directorate General for Scientific Research and Technological Development, Algeria. Publisher Copyright: {\textcopyright} 2022, Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan. All rights reserved.",

year = "2022",

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language = "English",

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pages = "131--152",

journal = "Proceedings of the Institute of Mathematics and Mechanics",

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AU - Redouane, Kelthoum Lina

AU - Arar, Nouria

AU - Al-Mdallal, Qasem

N1 - Funding Information: K.L. Redouane and N. Arar acknowledge support from Directorate General for Scientific Research and Technological Development, Algeria. Publisher Copyright: © 2022, Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan. All rights reserved.

PY - 2022

Y1 - 2022

N2 - This work is devoted to the development of a Galerkin-type approximation of the solution of parabolic reaction-diffusion problems, utilizing cubic B-Spline functions and a finite difference scheme. An error estimate for the semi discrete weak Galerkin scheme is established. A Von Neumann stability study of the proposed fully discrete Crank Nicolson scheme is also performed. In addition, examples are used to validate the proposed approximation. The numerical results produced demonstrate the procedure’s efficacy and are in good agreement with the exact solution.

AB - This work is devoted to the development of a Galerkin-type approximation of the solution of parabolic reaction-diffusion problems, utilizing cubic B-Spline functions and a finite difference scheme. An error estimate for the semi discrete weak Galerkin scheme is established. A Von Neumann stability study of the proposed fully discrete Crank Nicolson scheme is also performed. In addition, examples are used to validate the proposed approximation. The numerical results produced demonstrate the procedure’s efficacy and are in good agreement with the exact solution.

KW - Cubic B-splines

KW - Finite Difference Scheme

KW - Finite differences

KW - Galerkin method

KW - Parabolic problem

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DO - 10.30546/2409-4994.48.2022.131152

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SN - 2409-4986

VL - 48

SP - 131

EP - 152

JO - Proceedings of the Institute of Mathematics and Mechanics

JF - Proceedings of the Institute of Mathematics and Mechanics

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AN EFFICIENT NUMERICAL METHOD BASED ON CUBIC B-SPLINE FOR TIME DEPENDENT PROBLEM WITH SMALL PARAMETER

Abstract

Keywords

ASJC Scopus subject areas

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