BLUES iteration applied to nonlinear ordinary differential equations for wave propagation and heat transfer
Research output: Contribution to journal › Journal article › Research › peer-review
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.
Original language | English |
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Article number | 025702 |
Journal | Journal of Physics A: Mathematical and Theoretical |
Volume | 54 |
Issue number | 2 |
ISSN | 1751-8113 |
DOIs | |
Publication status | Published - Dec 2020 |
Bibliographical note
Publisher Copyright:
© 2020 The Author(s). Published by IOP Publishing Ltd.
- analytic approximation, fractional differential equation, iteration method, nonlinear differential equations, traveling wavefront
Research areas
ID: 371847838