New solutions of fractional-order Burger-Huxley equation

Mustafa Inc; Mohammad Partohaghighi; Mehmet Ali Akinlar; Paraveen Agarwal; Yu Ming Chu

doi:10.1016/j.rinp.2020.103290

New solutions of fractional-order Burger-Huxley equation

Mustafa Inc
, Mohammad Partohaghighi
, Mehmet Ali Akinlar
, Paraveen Agarwal
, Yu Ming Chu

Firat University
China Medical University Taichung
University of Bonab
Yildiz Technical University
International College of Engineering
Huzhou University
Changsha University of Science and Technology

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

34 Scopus citations

Abstract

A simple and powerful numerical method is proposed for solving the time-fractional Burger-Huxley equation (TFBH) equation within Caputo type fractional derivative. A fictitious coordinate θ is applied into the equation in order to convert the dependent variable u(x,t) into a new variable with an extra dimension. In the new space with the added fictitious dimension, a combination of the method of line and group preserving scheme (GPS) is introduced to find the approximate solutions. The reliability and accuracy of this scheme has been shown through some examples of the TFBH equation.

Original language	English
Article number	103290
Journal	Results in Physics
Volume	18
DOIs	https://doi.org/10.1016/j.rinp.2020.103290
State	Published - Sep 2020
Externally published	Yes

Keywords

Burger-Huxley equation
Caputo derivative
Fictitious time integration
Group preserving

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10.1016/j.rinp.2020.103290

Cite this

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title = "New solutions of fractional-order Burger-Huxley equation",

abstract = "A simple and powerful numerical method is proposed for solving the time-fractional Burger-Huxley equation (TFBH) equation within Caputo type fractional derivative. A fictitious coordinate θ is applied into the equation in order to convert the dependent variable u(x,t) into a new variable with an extra dimension. In the new space with the added fictitious dimension, a combination of the method of line and group preserving scheme (GPS) is introduced to find the approximate solutions. The reliability and accuracy of this scheme has been shown through some examples of the TFBH equation.",

keywords = "Burger-Huxley equation, Caputo derivative, Fictitious time integration, Group preserving",

author = "Mustafa Inc and Mohammad Partohaghighi and Akinlar, \{Mehmet Ali\} and Paraveen Agarwal and Chu, \{Yu Ming\}",

note = "Publisher Copyright: {\textcopyright} 2020 The Authors",

year = "2020",

month = sep,

doi = "10.1016/j.rinp.2020.103290",

language = "English",

volume = "18",

journal = "Results in Physics",

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T1 - New solutions of fractional-order Burger-Huxley equation

AU - Inc, Mustafa

AU - Partohaghighi, Mohammad

AU - Akinlar, Mehmet Ali

AU - Agarwal, Paraveen

AU - Chu, Yu Ming

PY - 2020/9

Y1 - 2020/9

N2 - A simple and powerful numerical method is proposed for solving the time-fractional Burger-Huxley equation (TFBH) equation within Caputo type fractional derivative. A fictitious coordinate θ is applied into the equation in order to convert the dependent variable u(x,t) into a new variable with an extra dimension. In the new space with the added fictitious dimension, a combination of the method of line and group preserving scheme (GPS) is introduced to find the approximate solutions. The reliability and accuracy of this scheme has been shown through some examples of the TFBH equation.

AB - A simple and powerful numerical method is proposed for solving the time-fractional Burger-Huxley equation (TFBH) equation within Caputo type fractional derivative. A fictitious coordinate θ is applied into the equation in order to convert the dependent variable u(x,t) into a new variable with an extra dimension. In the new space with the added fictitious dimension, a combination of the method of line and group preserving scheme (GPS) is introduced to find the approximate solutions. The reliability and accuracy of this scheme has been shown through some examples of the TFBH equation.

KW - Burger-Huxley equation

KW - Caputo derivative

KW - Fictitious time integration

KW - Group preserving

UR - https://www.scopus.com/pages/publications/85089907848

U2 - 10.1016/j.rinp.2020.103290

DO - 10.1016/j.rinp.2020.103290

M3 - Article

AN - SCOPUS:85089907848

SN - 2211-3797

VL - 18

JO - Results in Physics

JF - Results in Physics

M1 - 103290

ER -

New solutions of fractional-order Burger-Huxley equation

Abstract

Keywords

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