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Zeitschrift für Naturforschung A

A Journal of Physical Sciences

Editor-in-Chief: Holthaus, Martin

Editorial Board: Fetecau, Corina / Kiefer, Claus

IMPACT FACTOR 2017: 1.414

CiteScore 2018: 1.15

SCImago Journal Rank (SJR) 2018: 0.370
Source Normalized Impact per Paper (SNIP) 2018: 0.431

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Volume 67, Issue 6-7


On the Hybrid of Fourier Transform and Adomian Decomposition Method for the Solution of Nonlinear Cauchy Problems of the Reaction-Diffusion Equation

Salman Nourazar / Akbar Nazari-Golshan / Ahmet Yıldırım
  • University of South Florida, Department of Mathematics and Statistics, Tampa, FL 33620-5700 USA / Department of Mathematics, Science Faculty, Ege University, 35100 Bornova-Izmir, Turkey
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Maryam Nourazar
Published Online: 2014-06-02 | DOI: https://doi.org/10.5560/zna.2012-0025

The physical science importance of the Cauchy problem of the reaction-diffusion equation appears in the modelling of a wide variety of nonlinear systems in physics, chemistry, ecology, biology, and engineering. A hybrid of Fourier transform and Adomian decomposition method (FTADM) is developed for solving the nonlinear non-homogeneous partial differential equations of the Cauchy problem of reaction-diffusion. The results of the FTADM and the ADM are compared with the exact solution. The comparison reveals that for the same components of the recursive sequences, the errors associated with the FTADM are much lesser than those of the ADM. We show that as time increases the results of the FTADM approaches 1 with only six recursive terms. This is in agreement with the physical property of the density-dependent nonlinear diffusion of the Cauchy problem which is also in agreement with the exact solution.

The monotonic and very rapid convergence of the results of the FTADM towards the exact solution is shown to be much faster than that of the ADM

Keywords: Cauchy Reaction-Diffusion; Fourier Transformation; Adomian Decomposition Method; Non-Homogeneous Partial Differential Equation

About the article

Received: 2011-09-19

Revised: 2012-01-15

Published Online: 2014-06-02

Published in Print: 2012-07-01

Citation Information: Zeitschrift für Naturforschung A, Volume 67, Issue 6-7, Pages 355–362, ISSN (Online) 1865-7109, ISSN (Print) 0932-0784, DOI: https://doi.org/10.5560/zna.2012-0025.

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© 1946 – 2014: Verlag der Zeitschrift für Naturforschung. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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