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

Usama Ghafoor; Muhammad Abbas; Tayyaba Akram; Emad K. El-Shewy; Mahmoud A.E. Abdelrahman; Noura F. Abdo

doi:10.3390/fractalfract8020093

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

Usama Ghafoor
, Muhammad Abbas^*
, Tayyaba Akram
, Emad K. El-Shewy
, Mahmoud A.E. Abdelrahman
, Noura F. Abdo

^*Corresponding author for this work

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

5 Scopus citations

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 (Formula presented.) -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.

Original language	English
Article number	93
Journal	Fractal and Fractional
Volume	8
Issue number	2
DOIs	https://doi.org/10.3390/fractalfract8020093
State	Published - Feb 2024
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2024 by the authors.

Keywords

Caputo derivative
Crank–Nicolson finite difference technique
coupled Burgers equation
cubic B-spline
quasi-linearization

ASJC Scopus subject areas

Analysis
Statistical and Nonlinear Physics
Statistics and Probability

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10.3390/fractalfract8020093

Cite this

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

abstract = "The second order Burger{\textquoteright}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{\textquoteright}s formula, while the CBS technique with the help of a (Formula presented.) -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.",

keywords = "Caputo derivative, Crank–Nicolson finite difference technique, coupled Burgers equation, cubic B-spline, quasi-linearization",

author = "Usama Ghafoor and Muhammad Abbas and Tayyaba Akram and El-Shewy, \{Emad K.\} and Abdelrahman, \{Mahmoud A.E.\} and Abdo, \{Noura F.\}",

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doi = "10.3390/fractalfract8020093",

language = "English",

volume = "8",

journal = "Fractal and Fractional",

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T1 - An Efficient Cubic B-Spline Technique for Solving the Time Fractional Coupled Viscous Burgers Equation

AU - Ghafoor, Usama

AU - Abbas, Muhammad

AU - Akram, Tayyaba

AU - El-Shewy, Emad K.

AU - Abdelrahman, Mahmoud A.E.

AU - Abdo, Noura F.

PY - 2024/2

Y1 - 2024/2

N2 - 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 (Formula presented.) -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.

AB - 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 (Formula presented.) -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.

KW - Caputo derivative

KW - Crank–Nicolson finite difference technique

KW - coupled Burgers equation

KW - cubic B-spline

KW - quasi-linearization

UR - https://www.scopus.com/pages/publications/85187295109

U2 - 10.3390/fractalfract8020093

DO - 10.3390/fractalfract8020093

M3 - Article

AN - SCOPUS:85187295109

SN - 2504-3110

VL - 8

JO - Fractal and Fractional

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M1 - 93

ER -

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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