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

• Main Authors: Kumar Devendra, Sharma Ram Prakash
• Format: Article
• Language: English
• Published: De Gruyter 2016-06-01
• Series: Nonlinear Engineering
• Subjects: fractional newell-whitehead-segel equation; stripe pattern; caputo fractional derivative; homotopy analysis method; sumudu transform
• Online Access: https://doi.org/10.1515/nleng-2015-0032

The 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.