Integral iterative method for solving Newell-Whitehead-Segel equation / Nur' Atikah Khusairi, Nurul Izzaty Abdul Ghafar and Siti Nur Syafiqah Syed Huzaini

In this paper, the Integral Iterative Method (IIM) was execute for form exact solutions of the Newell-Whitehead-Segel equation. Newell-Whitehead-Segel equation can be recognized as nonlinear equation of an important model arising in fluid mechanics. But a nonlinear problem that contained strong nonlinearity and many are unknown. Usually, the iteration method would be used to solve nonlinear problems, but the convergence of iterations methods is very difficult to be achieved. The main objective of this report is approximating accuracy, reliability and ef¬ ficiency of JIM, when comparing Adomian Decomposition Method (ADM), Laplace Adomian Decomposition Method (LADM) and New Iterative Method (NIM). There are three problems of Newell-Whitehead-Segel equation chosen to be presented in an effective way. Numerous methods such as Variational Iteration Method (YIM), Homotopy Perturbation Method (HPM), and more methods have been used to solve this equation. However, in this paper, this equation is resolved using IIM. Our results show that IIM will be accurate, convenient and reliable in solving the nonlinear problems. IIM and were compared with the LADM, ADM and NIM, show the ability of Newell-Whitehead-Segel equation in solving nonlinear partial differential.Overall, this report made several contributions of Newell-Whitehead-Segel equation using IIM.First, for the first time, it is shown that IIM is better compared to NIM and LADM, which is absolutely convergence for the range of utility of the power series and closest to zero for the result of error value. Second, it is demonstrated that the error of JIM and NIM are compatible since the value of u(x,t) are close to zero compared to ADM. Third, it is concluded that HM solution could generate the same results with the exact solution. Based on the calculation, JIM is simpler and efficient implement for resolve varied category of non-linear differential and in¬ tegral equations, since this method only use direct integration method to derive the solution and the results were successfully explained.