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Numerical approximation of Newell-Whitehead-Segel equation of fractional order

Numerical approximation of Newell-Whitehead-Segel equation of fractional order AbstractThe aim of the present work is to propose a user friendly approach based on homotopy analysis method combined with Sumudu transform method to drive analytical and numerical solutions of the fractional Newell-Whitehead-Segel amplitude equation which describes the appearance of the stripe patterns in 2-dimensional systems. The coupling of homotopy analysis method with Sumudu transform algorithm makes the calculation very easy. The proposed technique gives an analytic solution in the form of series which converge very fastly. The analytical and numerical results reveal that the coupling of homotopy analysis technique with Sumudu transform algorithm is very easy to apply and highly accuratewhen apply to non-linear differential equation of fractional order. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Nonlinear Engineering de Gruyter

Numerical approximation of Newell-Whitehead-Segel equation of fractional order

Kumar, Devendra; Sharma, Ram Prakash
Nonlinear Engineering , Volume 5 (2): 6 – Jun 1, 2016
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Publisher
de Gruyter
Copyright
© 2016 Walter de Gruyter GmbH, Berlin/Boston
ISSN
2192-8029
eISSN
2192-8029
DOI
10.1515/nleng-2015-0032
Publisher site
See Article on Publisher Site

Abstract

AbstractThe aim of the present work is to propose a user friendly approach based on homotopy analysis method combined with Sumudu transform method to drive analytical and numerical solutions of the fractional Newell-Whitehead-Segel amplitude equation which describes the appearance of the stripe patterns in 2-dimensional systems. The coupling of homotopy analysis method with Sumudu transform algorithm makes the calculation very easy. The proposed technique gives an analytic solution in the form of series which converge very fastly. The analytical and numerical results reveal that the coupling of homotopy analysis technique with Sumudu transform algorithm is very easy to apply and highly accuratewhen apply to non-linear differential equation of fractional order.

Journal

Nonlinear Engineering – de Gruyter

Published: Jun 1, 2016

References

  • A comparison between the reduced differential transform method and the Adomian decomposition method for the Newell-Whitehead-Segel equation
  • Super symmetric pairing of kinks for polynomial nonlinearities
  • Rayleigh-Benard Convection: Structures and Dynamics
  • Numerical methods for non linear partial differential equations of fractional order
  • General Aspect Of Pattern Formation