An Efficient Cubic B-Spline Technique for Solving the Time Fractional Coupled Viscous Burgers Equation

Author:

Ghafoor Usama1,Abbas Muhammad1ORCID,Akram Tayyaba2ORCID,El-Shewy Emad K.34ORCID,Abdelrahman Mahmoud A. E.56ORCID,Abdo Noura F.56

Affiliation:

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

2. Center of Excellence in Theoretical and Computational Science (TaCS-CoS), Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand

3. Department of Physics, College of Science, Taibah University, Al-Madinah Al-Munawarah 41477, Saudi Arabia

4. Theoretical Physics Group, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

5. Department of Mathematics, College of Science, Taibah University, Al-Madinah Al-Munawarah 41477, Saudi Arabia

6. Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

Abstract

The second order Burger’s equation model is used to study the turbulent fluids, suspensions, shock waves, and the propagation of shallow water waves. In the present research, we investigate a numerical solution to the time fractional coupled-Burgers equation (TFCBE) using Crank–Nicolson and the cubic B-spline (CBS) approaches. The time derivative is addressed using Caputo’s formula, while the CBS technique with the help of a θ-weighted scheme is utilized to discretize the first- and second-order spatial derivatives. The quasi-linearization technique is used to linearize the non-linear terms. The suggested scheme demonstrates unconditionally stable. Some numerical tests are utilized to evaluate the accuracy and feasibility of the current technique.

Funder

Research & Innovation in the Ministry of Education in Saudi Arabia

Publisher

MDPI AG

Subject

Statistics and Probability,Statistical and Nonlinear Physics,Analysis

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