The integral iterative method for approximate solution of Newell-Whitehead-Segel equation / Mat Salim Selamat … [et.al.]

Most numerical methods require very extensive calculations and use very large computer memory. The resulting numerical solution is also very sensitive to any small changes in the parameters present in the differential equation. This paper presents research finding that has been conducted with two objectives. First objective is to solve the Newell-Whitehead-Segel (NWS) equation using integral iterative method (IIM). Second objective is to determine the accuracy, reliability and efficiency of IIM by compared to the exact solution and other existing results obtained by other methods such as New Iterative Method (NIM), Adomian decomposition method (ADM) and Laplace Adomian decomposition method (LADM). This iterative method was calculated based on the integral operator, that is the inverse of the differential operator in the problem under consideration. The analytical solution of the equation was calculated in the form of power series solution. Results of this research has identified that the method is simpler in its computational procedures and needs shorter time to be completed than the other methods. It does not require discretization, linearization or any restrictive assumption in order to provide analytical and approximate solution. The technique provides in this research introduced a straightforward and powerful mathematical tool for solving various differential equations.