Advanced Methods for Conformable Time-Fractional Differential Equations: Logarithmic Non-Polynomial Splines-Reference-Cited by-同舟云学术

Advanced Methods for Conformable Time-Fractional Differential Equations: Logarithmic Non-Polynomial Splines

Published:2024-08-13 Issue:8 Volume:13 Page:551
ISSN:2075-1680
Container-title:Axioms
language:en
Short-container-title:Axioms

Author:

Yousif Majeed A.¹^ORCID,Agarwal Ravi P.²^ORCID,Mohammed Pshtiwan Othman³⁴^ORCID,Lupas Alina Alb⁵^ORCID,Jan Rashid⁶⁷^ORCID,Chorfi Nejmeddine⁸^ORCID

Affiliation:

1. Department of Mathematics, College of Education, University of Zakho, Duhok 42001, Iraq

2. Department of Mathematics and Systems Engineering, Florida Institute of Technology, Melbourne, FL 32901, USA

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

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

5. Department of Mathematics and Computer Science, University of Oradea, 410087 Oradea, Romania

6. Institute of Energy Infrastructure (IEI), Department of Civil Engineering, College of Engineering, Universiti Tenaga Nasional (UNITEN), Putrajaya Campus, Jalan IKRAM-UNITEN, Kajang 43000, Malaysia

7. Mathematics Research Center, Near East University TRNC, Mersin 10, Nicosia 99138, Turkey

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

Abstract

In this study, we present a numerical method named the logarithmic non-polynomial spline method. This method combines conformable derivative, finite difference, and non-polynomial spline techniques to solve the nonlinear inhomogeneous time-fractional Burgers–Huxley equation. The developed numerical scheme is characterized by a sixth-order convergence and conditional stability. The accuracy of the method is demonstrated with 3D mesh plots, while the effects of time and fractional order are shown in 2D plots. Comparative evaluations with the cubic B-spline collocation method are provided. To illustrate the suitability and effectiveness of the proposed method, two examples are tested, with the results are evaluated using L2 and L∞ norms.

Funder

University of Oradea, Romania

Publisher

MDPI AG

Link

https://www.mdpi.com/2075-1680/13/8/551/pdf

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