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

Affiliation(s)

Department of Mathematics, Faculty of Science & Mansoura University, Mansoura, Egypt.

Department of Engineering Mathematics & Physics, Engineering Faculty, Cairo University, Giza, Egypt.

Department of Electrical & Computer Engineering, Engineering Faculty, Effat University, Jeddah, KSA.

Department of Mathematics, Faculty of Science & Mansoura University, Mansoura, Egypt.

Department of Engineering Mathematics & Physics, Engineering Faculty, Cairo University, Giza, Egypt.

Department of Electrical & Computer Engineering, Engineering Faculty, Effat University, Jeddah, KSA.

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

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

Cite this paper

M. Hamed, M. El-Twail, B. El-desouky and M. El-Beltagy, "Solution of Nonlinear Stochastic Langevin’s Equation Using WHEP, Pickard and HPM Methods,"*Applied Mathematics*, Vol. 5 No. 3, 2014, pp. 398-412. doi: 10.4236/am.2014.53041.

M. Hamed, M. El-Twail, B. El-desouky and M. El-Beltagy, "Solution of Nonlinear Stochastic Langevin’s Equation Using WHEP, Pickard and HPM Methods,"

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