the elzaki homotopy perturbation method for partial differential equations

in this paper, elzaki homotopy perturbation method is employed for solving linear and nonlinear differential equations with a variable coffecient. this method is a combination of elzaki transform and homotopy perturbation method. the aim of using elzaki transform is to overcome the deficiencies that mainly caused by unsatised conditions in some semi-analytical methods such as homotopy perturbation method, variational iteration method and adomian decomposition method. the approximate solutions obtained by means of elzaki homotopy perturbation method were compared in a wide range of problem's domain with those results obtained by homotopy perturbation method. the comparison shows a precise agreement between the exact solutions and the obtained results by this new method as an applicable one, which needs less computations and is much easier and more convenient than others. so, it can be widely used in engineering and other branches of science.