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.