SOLVING LINEAR AND NONLINEAR KLEIN-GORDON EQUATIONS BY NEW PERTURBATION ITERATION TRANSFORM METHOD

Abstract

We present an effective algorithm to solve the Linear and Nonlinear KleinGordon equation, which is based on the Perturbation Iteration Transform Method (PITM).The Klein-Gordon equation is the name given to the equation of motion of a quantumscalar or pseudo scalar field, a field whose quanta are spin-less particles. It describes thequantum amplitude for finding a point particle in various places, the relativistic wavefunction, but the particle propagates both forwards and backwards in time. The Perturbation Iteration Transform Method (PITM) is a combined form of the Laplace TransformMethod and Perturbation Iteration Algorithm. The method provides the solution in theform of a rapidly convergent series. Some numerical examples are used to illustrate thepreciseness and effectiveness of the proposed method. The results show that the PITMis very efficient, simple and can be applied to other nonlinear problems.