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Solving random diffusion models with nonlinear perturbations by the Wiener–Hermite expansion method
- Source :
-
Computers & Mathematics with Applications . Apr2011, Vol. 61 Issue 8, p1946-1950. 5p. - Publication Year :
- 2011
-
Abstract
- Abstract: This paper deals with the construction of approximate series solutions of random nonlinear diffusion equations where nonlinearity is considered by means of a frank small parameter and uncertainty is introduced through white noise in the forcing term. For the simpler but important case in which the diffusion coefficient is time independent, we provide a Gaussian approximation of the solution stochastic process by taking advantage of the Wiener–Hermite expansion together with the perturbation method. In addition, approximations of the main statistical functions associated with a solution, such as the mean and variance, are computed. Numerical values of these functions are compared with respect to those obtained by applying the Runge–Kutta second-order stochastic scheme as an illustrative example. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 08981221
- Volume :
- 61
- Issue :
- 8
- Database :
- Academic Search Index
- Journal :
- Computers & Mathematics with Applications
- Publication Type :
- Academic Journal
- Accession number :
- 59943740
- Full Text :
- https://doi.org/10.1016/j.camwa.2010.07.057