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
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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