Abstract
THE ITERATION METHOD FOR STUDYING THE KLEIN-GORDON EQUATIONS
Ammarah Marriyam*, Mirza Naveed Jahngeer Baig, Nasir Khan, Babar Hussain, Maira Mukhlis, Muhammad Imran Shahid
ABSTRACT
In recently, different iterative methods viz Adomian decomposition method, variational iteration method, Homotopy Pertubation method etc. have been developed for solving linear and nonlinear ordinary and PDEs. Recently Versha and Jafery proposed an iterative method called the New Iterative Method (NIM) and successfully applied it to linear and nonlinear PDEs of integer and fractional order. In this paper we propose an efficient modification to the NIM and applied the modified NIM to obtain improved form solutions of various types of linear and nonlinear Klein-Gordon equations. The proposed modification is easy to use and we obtained excellent performance in comparison with the existing iterative methods that have been traditionally used in finding the solution of linear and nonlinear Klein-Gordon equations. The main feature of the modified NIM is that it reduces the size of calculations and gives the solution rapidly while still maintaining high degree of accuracy.
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