W. T. Coffey and Y. P Kalmykov, “The Langevin Equation, with Applications to Stochastic Problems in Physics, Chemistry and Electrical Engineering,” 3rd Edition, World Scientific Publishing Company, Singapore City, 2012.

has been cited by the following article:

• TITLE: Solution of Nonlinear Stochastic Langevin’s Equation Using WHEP, Pickard and HPM Methods

  AUTHORS: Maha Hamed, Magdy A. El-Twail, Beih El-desouky, Mohamed A. El-Beltagy

  KEYWORDS: Nonlinear Stochastic D.E; Langevin’s Equation; WHEP Technique; Picard Approximation; HPM Technique

  JOURNAL NAME: Applied Mathematics, Vol.5 No.3, February 11, 2014

  ABSTRACT: This paper introduces analytical and numerical solutions of the nonlinear Langevin’s equation under square nonlinearity with stochastic non-homogeneity. The solution is obtained by using the Wiener-Hermite expansion with perturbation (WHEP) technique, and the results are compared with those of Picard iterations and the homotopy perturbation method (HPM). The WHEP technique is used to obtain up to fourth order approximation for different number of corrections. The mean and variance of the solution are obtained and compared among the different methods, and some parametric studies are done by using Matlab.