Semi-analytical iterative method for solving Klein-Gordon equation / Afifah Muhidzir, Nor Nazierah Abd Razak and Zakila Amira Hassanuddin - Muhidzir, Afifah; Abd Razak, Nor Nazierah; Hassanuddin, Zakila Amira (2019)
In this paper, the Semi Analytical Iterative Method (SAIM) was applied to generate approximate solutions of the Klein-Gordon equations. Klein-Gordon equation is known as a relativistic wave equation. Various methods have been approached to solve this equation such as Modified Adomian Decomposition Method (MADM), Variation Iterative Method (VIM), Homotopy Perturbation Method (HPM) and many more. The problem is that the convergence of iteration method is very difficult to achieve since the iteration method that is delicate to the initial conditions and the number of unknowns in the differential equation and the calculation seems quite difficult to solve. Comparisons with the exact solutions obtained by MADM, VIM and HPM show the potential of SAIM in solving Klein-Gordon equations. As a result, SAIM is reliable and simple calculation. This method only use direct differentiation method and the results were successfully explained.