Analytical approaches to space- and time-fractional coupled Burgers’ equations

We solve the one- and two-dimensional fractional coupled Burgers’ equations (FCBEs) by three different methods. The proposed methods are the Laplace–Adomian decomposition method (LADM), the Laplace-variational iteration method (LVIM) and the reduced differential transform method (RDTM). The solution...

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Bibliographic Details
Published in:Pramāṇa 2019-03, Vol.92 (3), Article 38
Main Authors: Ahmed, Hoda F, Bahgat, M S M, Zaki, Mofida
Format: Article
Language:English
Subjects:
Astronomy
Astrophysics and Astroparticles
Burgers equation
Iterative methods
Mathematical analysis
Observations and Techniques
Physics
Physics and Astronomy
Series (mathematics)
Two dimensional analysis
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Summary:We solve the one- and two-dimensional fractional coupled Burgers’ equations (FCBEs) by three different methods. The proposed methods are the Laplace–Adomian decomposition method (LADM), the Laplace-variational iteration method (LVIM) and the reduced differential transform method (RDTM). The solutions are obtained as rapidly convergent series with simply calculable terms. Numerical studies of the application of these approaches for a number of sample problems are given and are illustrated graphically. With these methods, it is possible to investigate the nature of solutions when the fractional derivative parameters are changed. The numerical results reveal the effectiveness and the correctness of the proposed methods.
ISSN:0304-4289
0973-7111
DOI:10.1007/s12043-018-1693-z