International Conference on Mathematical Applications in Engineering (ICMAE’10), (2010), Kuala Lumpur, Malaysia.
Recently nonlinear partial differential equation has attracted scientist’s attention, which means that this type of equations playes a keyrole in many fields such as engineering. In this work we considered the variational iteration method which is an usefull instrument for solving partial differential equations
with polynomials nonlinearities. This method first proposed by He and it was used for solving many kinds of situations. We have made a modification on the (VIM) in order to apply it for those PDE’s with logarithmic nonlinearities. We employed this modified method for solving the Klein-Gordon equation and the Kolmogorov-Petrovskii-Piskunov equation which are two applicable equations. Klein-Gordon was named after the physicists Oskar Klein and Walter Gordon, who in 1927 proposed that it describes relativistic electrons. One of the best known model equations with dissipation is the equation suggested in 1937 by Kolmogorov, Petrovskii and Piskunov. This equation describes such phenomena as combustion (physics) and propagation of concentration waves. This method could be used for any nonlinear partial differential equation with logarithmic nonlinearitie. The results reveal that the method is very effective and convenient.