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

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

## M. KHALID, M. SULTANA, F. ZAIDI, A. UROOSA

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## Abstract

We present an eective algorithm to solve the Linear and Nonlinear Klein-

Gordon 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 quantum

scalar or pseudo scalar eld, a eld whose quanta are spin-less particles. It describes the

quantum amplitude for nding a point particle in various places, the relativistic wave

function, but the particle propagates both forwards and backwards in time. The Pertur-

bation Iteration Transform Method (PITM) is a combined form of the Laplace Transform

Method and Perturbation Iteration Algorithm. The method provides the solution in the

form of a rapidly convergent series. Some numerical examples are used to illustrate the

preciseness and eectiveness of the proposed method. The results show that the PITM

is very ecient, simple and can be applied to other nonlinear problems.

## Keywords

Perturbation Iteration Algorithm, Laplace Transform Method, Linear and Nonlinear Klein-Gordon Equations.