Semi-analytical iterative method for solving Klein-Gordon equation / Afifah Muhidzir, Nor Nazierah Abd Razak and Zakila Amira Hassanuddin

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.