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

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

Department of Electrical & Computer Engineering, Engineering Faculty, Effat University, Jeddah, KSA.
Department of Engineering Mathematics & Physics, Engineering Faculty, Cairo University, Giza, Egypt.
Department of Mathematics, Faculty of Science & Mansoura University, Mansoura, Egypt.

DOI: 10.4236/am.2014.53041                

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.

Keywords

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

Conflicts of Interest

The authors declare no conflicts of interest.

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