Homotopy Perturbation-Laplace Method for Solving Random Ordinary Differential Equations

In this paper, the homotopy perturbation method will be used in connection with Laplace transformation method to give a hybrid approach as a modification of the homotopy perturbation method to find the approximate solutions of random ordinary differential equations. The approximate solution is proved also to converge to the exact solution, in which the analysis of the proof is based on mean square convergence of the sequence of a random process. The proposed hybrid approach is effectively used to find the exact solution for the considered examples, which are simulated and solved using two generations of Brownian motion with a total length of signal processing, namely 500 and 1000 generations.