Exact solution of nonlinear Newell–Whitehead–Segel equation using semi‐analytical approach

Abstract

This paper proposed a reliable semi‐analytical approach, namely, the reduced differential transform method, to evaluate the exact solution of the Newell–Whitehead–Segel equation. It models chemical reactions, Rayleigh–Bernard convection, and Faraday instability. The existing analytical approaches in the literature do not deal effectively with nonlinear terms and boundary condition. To show the effectiveness and reliability of the proposed method, this paper discusses three cases. The obtained results are more accurate than the other existing methods available in the literature.The accuracy of solution obtained is of 10−12 order approximately in each of the three cases. The analytical solution is also compared with an exact solution, which shows an excellent agreement. The paper also discusses error analysis for the obtained series solution with the straightforward applicability, with less cost and computational effort.