BLUES iteration applied to nonlinear ordinary differential equations for wave propagation and heat transfer

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BLUES iteration applied to nonlinear ordinary differential equations for wave propagation and heat transfer. / Berx, Jonas; Indekeu, Joseph O.

In: Journal of Physics A: Mathematical and Theoretical, Vol. 54, No. 2, 025702, 12.2020.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Berx, J & Indekeu, JO 2020, 'BLUES iteration applied to nonlinear ordinary differential equations for wave propagation and heat transfer', Journal of Physics A: Mathematical and Theoretical, vol. 54, no. 2, 025702. https://doi.org/10.1088/1751-8121/abcf57

APA

Berx, J., & Indekeu, J. O. (2020). BLUES iteration applied to nonlinear ordinary differential equations for wave propagation and heat transfer. Journal of Physics A: Mathematical and Theoretical, 54(2), [025702]. https://doi.org/10.1088/1751-8121/abcf57

Vancouver

Berx J, Indekeu JO. BLUES iteration applied to nonlinear ordinary differential equations for wave propagation and heat transfer. Journal of Physics A: Mathematical and Theoretical. 2020 Dec;54(2). 025702. https://doi.org/10.1088/1751-8121/abcf57

Author

Berx, Jonas ; Indekeu, Joseph O. / BLUES iteration applied to nonlinear ordinary differential equations for wave propagation and heat transfer. In: Journal of Physics A: Mathematical and Theoretical. 2020 ; Vol. 54, No. 2.

Bibtex

@article{e86b9406aa64426fbe48cda76f023e2a,
title = "BLUES iteration applied to nonlinear ordinary differential equations for wave propagation and heat transfer",
abstract = "The iteration sequence based on the BLUES (Beyond Linear Use of Equation Superposition) function method for calculating analytic approximants to solutions of nonlinear ordinary differential equations with sources is elaborated upon. Diverse problems in physics are studied and approximate analytic solutions are found. We first treat a damped driven nonlinear oscillator and show that the method can correctly reproduce oscillatory behavior. Next, a fractional differential equation describing heat transfer in a semi-infinite rod with Stefan-Boltzmann cooling is handled. In this case, a detailed comparison is made with the Adomian decomposition method, the outcome of which is favourable for the BLUES method. As a final problem, the Fisher equation from population biology is dealt with. For all cases, it is shown that the solutions converge exponentially fast to the numerically exact solution, either globally or, for the Fisher problem, locally.",
keywords = "analytic approximation, fractional differential equation, iteration method, nonlinear differential equations, traveling wavefront",
author = "Jonas Berx and Indekeu, {Joseph O.}",
note = "Publisher Copyright: {\textcopyright} 2020 The Author(s). Published by IOP Publishing Ltd.",
year = "2020",
month = dec,
doi = "10.1088/1751-8121/abcf57",
language = "English",
volume = "54",
journal = "Journal of Physics A: Mathematical and Theoretical",
issn = "1751-8113",
publisher = "Institute of Physics Publishing Ltd",
number = "2",

}

RIS

TY - JOUR

T1 - BLUES iteration applied to nonlinear ordinary differential equations for wave propagation and heat transfer

AU - Berx, Jonas

AU - Indekeu, Joseph O.

N1 - Publisher Copyright: © 2020 The Author(s). Published by IOP Publishing Ltd.

PY - 2020/12

Y1 - 2020/12

N2 - The iteration sequence based on the BLUES (Beyond Linear Use of Equation Superposition) function method for calculating analytic approximants to solutions of nonlinear ordinary differential equations with sources is elaborated upon. Diverse problems in physics are studied and approximate analytic solutions are found. We first treat a damped driven nonlinear oscillator and show that the method can correctly reproduce oscillatory behavior. Next, a fractional differential equation describing heat transfer in a semi-infinite rod with Stefan-Boltzmann cooling is handled. In this case, a detailed comparison is made with the Adomian decomposition method, the outcome of which is favourable for the BLUES method. As a final problem, the Fisher equation from population biology is dealt with. For all cases, it is shown that the solutions converge exponentially fast to the numerically exact solution, either globally or, for the Fisher problem, locally.

AB - The iteration sequence based on the BLUES (Beyond Linear Use of Equation Superposition) function method for calculating analytic approximants to solutions of nonlinear ordinary differential equations with sources is elaborated upon. Diverse problems in physics are studied and approximate analytic solutions are found. We first treat a damped driven nonlinear oscillator and show that the method can correctly reproduce oscillatory behavior. Next, a fractional differential equation describing heat transfer in a semi-infinite rod with Stefan-Boltzmann cooling is handled. In this case, a detailed comparison is made with the Adomian decomposition method, the outcome of which is favourable for the BLUES method. As a final problem, the Fisher equation from population biology is dealt with. For all cases, it is shown that the solutions converge exponentially fast to the numerically exact solution, either globally or, for the Fisher problem, locally.

KW - analytic approximation

KW - fractional differential equation

KW - iteration method

KW - nonlinear differential equations

KW - traveling wavefront

UR - http://www.scopus.com/inward/record.url?scp=85099108070&partnerID=8YFLogxK

U2 - 10.1088/1751-8121/abcf57

DO - 10.1088/1751-8121/abcf57

M3 - Journal article

AN - SCOPUS:85099108070

VL - 54

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 2

M1 - 025702

ER -

ID: 371847838