An efficient numerical technique for solving time fractional Burgers equation

Tayyaba Akram; Muhammad Abbas; Muhammad Bilal Riaz; Ahmad Izani Ismail; Norhashidah Mohd Ali

doi:10.1016/j.aej.2020.01.048

An efficient numerical technique for solving time fractional Burgers equation

Tayyaba Akram
, Muhammad Abbas^*
, Muhammad Bilal Riaz
, Ahmad Izani Ismail
, Norhashidah Mohd Ali

^*Corresponding author for this work

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

72 Scopus citations

Abstract

A finite difference scheme which depends on a new approximation based on an extended cubic B-spline for the second order derivative is used to calculate the numerical outcomes of time fractional Burgers equation. The presented scheme uses Caputo's formulation for the time derivative. Finite difference method will be used to discretize the Caputo's fractional derivative. The proposed scheme will be shown to be unconditionally stable by Von-Neumann method. The convergence analysis of the numerical scheme will be presented of order O(h²+τ^2-α). The presented scheme is tested on four numerical examples. The numerical results are compared favorably with other computational schemes.

Original language	English
Pages (from-to)	2201-2220
Number of pages	20
Journal	Alexandria Engineering Journal
Volume	59
Issue number	4
DOIs	https://doi.org/10.1016/j.aej.2020.01.048
State	Published - Aug 2020
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2020 Faculty of Engineering, Alexandria University

Keywords

Caputo's derivative
Convergence
Extended cubic B-spline basis functions
Nonlinear time fractional Burgers equation
Stability

ASJC Scopus subject areas

General Engineering

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10.1016/j.aej.2020.01.048

Cite this

@article{c1085a49d19446bab40444b231a76bf7,

title = "An efficient numerical technique for solving time fractional Burgers equation",

abstract = "A finite difference scheme which depends on a new approximation based on an extended cubic B-spline for the second order derivative is used to calculate the numerical outcomes of time fractional Burgers equation. The presented scheme uses Caputo's formulation for the time derivative. Finite difference method will be used to discretize the Caputo's fractional derivative. The proposed scheme will be shown to be unconditionally stable by Von-Neumann method. The convergence analysis of the numerical scheme will be presented of order O(h2+τ2-α). The presented scheme is tested on four numerical examples. The numerical results are compared favorably with other computational schemes.",

keywords = "Caputo's derivative, Convergence, Extended cubic B-spline basis functions, Nonlinear time fractional Burgers equation, Stability",

author = "Tayyaba Akram and Muhammad Abbas and Riaz, \{Muhammad Bilal\} and Ismail, \{Ahmad Izani\} and Ali, \{Norhashidah Mohd\}",

note = "Publisher Copyright: {\textcopyright} 2020 Faculty of Engineering, Alexandria University",

year = "2020",

month = aug,

doi = "10.1016/j.aej.2020.01.048",

language = "English",

volume = "59",

pages = "2201--2220",

journal = "Alexandria Engineering Journal",

issn = "1110-0168",

number = "4",

}

TY - JOUR

T1 - An efficient numerical technique for solving time fractional Burgers equation

AU - Akram, Tayyaba

AU - Abbas, Muhammad

AU - Riaz, Muhammad Bilal

AU - Ismail, Ahmad Izani

AU - Ali, Norhashidah Mohd

PY - 2020/8

Y1 - 2020/8

N2 - A finite difference scheme which depends on a new approximation based on an extended cubic B-spline for the second order derivative is used to calculate the numerical outcomes of time fractional Burgers equation. The presented scheme uses Caputo's formulation for the time derivative. Finite difference method will be used to discretize the Caputo's fractional derivative. The proposed scheme will be shown to be unconditionally stable by Von-Neumann method. The convergence analysis of the numerical scheme will be presented of order O(h2+τ2-α). The presented scheme is tested on four numerical examples. The numerical results are compared favorably with other computational schemes.

AB - A finite difference scheme which depends on a new approximation based on an extended cubic B-spline for the second order derivative is used to calculate the numerical outcomes of time fractional Burgers equation. The presented scheme uses Caputo's formulation for the time derivative. Finite difference method will be used to discretize the Caputo's fractional derivative. The proposed scheme will be shown to be unconditionally stable by Von-Neumann method. The convergence analysis of the numerical scheme will be presented of order O(h2+τ2-α). The presented scheme is tested on four numerical examples. The numerical results are compared favorably with other computational schemes.

KW - Caputo's derivative

KW - Convergence

KW - Extended cubic B-spline basis functions

KW - Nonlinear time fractional Burgers equation

KW - Stability

UR - https://www.scopus.com/pages/publications/85080060437

U2 - 10.1016/j.aej.2020.01.048

DO - 10.1016/j.aej.2020.01.048

M3 - Article

AN - SCOPUS:85080060437

SN - 1110-0168

VL - 59

SP - 2201

EP - 2220

JO - Alexandria Engineering Journal

JF - Alexandria Engineering Journal

IS - 4

ER -

An efficient numerical technique for solving time fractional Burgers equation

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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