Solution of Newell-Whitehead-Segel equation by variational iteration method with He's polynomials

Volume 20, Issue 1, pp 21--29
Publication Date: August 28, 2019 Submission Date: June 09, 2019 Revision Date: July 01, 2019 Accteptance Date: July 23, 2019


Muhammad Nadeem - School of Mathematical Sciences , Dalian University of Technology, Dalian 116024, China. Shao-Wen Yao - School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, China. Nusrat Parveen - Department of Social Sciences, Govt. College University Faisalabad, Layyah Campus, Layyah 31200, Pakistan.


This article seeks to extend the variational iteration method (VIM) with He's polynomials for the approximate solution of nonlinear Newell-Whitehead-Segel equation (NWSE). Lagrange multiplier in correction functional is determined with the help of variational theory, and then homotopy perturbation method (HPM) is employed to dissolve the nonlinear terms. Thus a successful series is obtained with these iterations which are termed as He's polynomials. Result shows that this method is highly accurate and comes closer very quickly to the exact solution. We formulate three possible cases of NWSE to show the capability and ability of the present method. The valuable outcome discloses that the proposed strategy is very convenient, straightforward and can be utilized to linear and nonlinear problems.