Extension of Cubic B-Spline for Solving the Time-Fractional Allen–Cahn Equation in the Context of Mathematical Physics-Reference-Cited by-同舟云学术

Extension of Cubic B-Spline for Solving the Time-Fractional Allen–Cahn Equation in the Context of Mathematical Physics

Published:2024-03-05 Issue:3 Volume:12 Page:51
ISSN:2079-3197
Container-title:Computation
language:en
Short-container-title:Computation

Author:

Fatima Mubeen¹,Agarwal Ravi P.²^ORCID,Abbas Muhammad¹^ORCID,Mohammed Pshtiwan Othman³⁴^ORCID,Shafiq Madiha¹^ORCID,Chorfi Nejmeddine⁵^ORCID

Affiliation:

1. Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan

2. Department of Mathematics, Texas A & M University-Kingsville, Kingsville, TX 78363, USA

3. Department of Mathematics, College of Education, University of Sulaimani, Sulaymaniyah 46001, Iraq

4. Research and Development Center, University of Sulaimani, Sulaymaniyah 46001, Iraq

5. Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Abstract

A B-spline is defined by the degree and quantity of knots, and it is observed to provide a higher level of flexibility in curve and surface layout. The extended cubic B-spline (ExCBS) functions with new approximation for second derivative and finite difference technique are incorporated in this study to solve the time-fractional Allen–Cahn equation (TFACE). Initially, Caputo’s formula is used to discretize the time-fractional derivative, while a new ExCBS is used for the spatial derivative’s discretization. Convergence analysis is carried out and the stability of the proposed method is also analyzed. The scheme’s applicability and feasibility are demonstrated through numerical analysis.

Publisher

MDPI AG

Link

https://www.mdpi.com/2079-3197/12/3/51/pdf

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