en عمومى General كاربردي Applicable Nonlinear wave equations are more difficult to study mathematically and that no general analytical method for their solution exists. It is found that the Exponential Time Differencing (ETD) scheme requires the least steps to achieve a given accuracy, offers a speedy method at calculation time, and has exceptional stability properties in solving a nonlinear equation. This article explains how we applied the exponential integrators (ETDRK4) to semi-linear problems to solve the fifth-order KdV equation. To solve, we define a new integrating factor e^(-ik^5 t) and apply fast Fourier transform (FFT ) for spatial discretization. For this purpose, we solve the diagonal example of the fifth-order KdV equation via the exponential time differencing Runge-Kutta 4 method (ETDRK4). Implementation of the method is proposed by short Matlab programs. Exponential Methods, Integration Factor Methods, Exponential Time Differencing Methods, Runge-Kutta Method. 57 64 http://ijorlu.lahijan.iau.ir/browse.php?a_code=A-10-534-1&slc_lang=en&sid=1 M. Askaripour Lahiji lahiji1975@gmail.com 10031947532846001730 10031947532846001730 Yes Department of Mathematics, Astaneh Ashrafieh Branch, Islamic Azad University, Astaneh Ashrafieh, Iran M. Mirzaei Chalakei mohsenmirzaee37@yahoo.com 10031947532846001731 10031947532846001731 No Department of Mathematics, Astaneh Ashrafieh Branch, Islamic Azad University, Astaneh Ashrafieh, Iran E. Amoupour amoupour@yahoo.com 10031947532846001732 10031947532846001732 No 2Department of Physics, Roudsar and Amlash Branch, Islamic Azad University , Roudsar, Iran