Statistical measures approximations for the Gaussian part of the stochastic nonlinear damped Duffing oscillator solution process under the application of Wiener Hermite expansion linked by the multi-step differential transformed method
Zait,, R., El-Shekhipy, A., Abdo, N. (2016). Statistical measures approximations for the Gaussian part of the stochastic nonlinear damped Duffing oscillator solution process under the application of Wiener Hermite expansion linked by the multi-step differential transformed method. EKB Journal Management System, 24(3), 437-448. doi: 10.1016/j.joems.2015.11.002
R. A. Zait,; A. A. El-Shekhipy; N. M. Abdo. "Statistical measures approximations for the Gaussian part of the stochastic nonlinear damped Duffing oscillator solution process under the application of Wiener Hermite expansion linked by the multi-step differential transformed method". EKB Journal Management System, 24, 3, 2016, 437-448. doi: 10.1016/j.joems.2015.11.002
Zait,, R., El-Shekhipy, A., Abdo, N. (2016). 'Statistical measures approximations for the Gaussian part of the stochastic nonlinear damped Duffing oscillator solution process under the application of Wiener Hermite expansion linked by the multi-step differential transformed method', EKB Journal Management System, 24(3), pp. 437-448. doi: 10.1016/j.joems.2015.11.002
Zait,, R., El-Shekhipy, A., Abdo, N. Statistical measures approximations for the Gaussian part of the stochastic nonlinear damped Duffing oscillator solution process under the application of Wiener Hermite expansion linked by the multi-step differential transformed method. EKB Journal Management System, 2016; 24(3): 437-448. doi: 10.1016/j.joems.2015.11.002

Statistical measures approximations for the Gaussian part of the stochastic nonlinear damped Duffing oscillator solution process under the application of Wiener Hermite expansion linked by the multi-step differential transformed method

Journal of the Egyptian Mathematical Society
Volume 24, Issue 3, 2016, Page 437-448  XML PDF (5.43 MB)
DOI: 10.1016/j.joems.2015.11.002
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Authors
R. A. Zait,; A. A. El-Shekhipy; N. M. Abdo
Mathematics Department, Faculty of science, Minia University, El-Minia, Egypt
Abstract
In this paper, the stochastic Wiener Hermite expansion (WHE) is used to find the statistical
measures (mean and variance) of the first order stochastic approximation (Gaussian part) of
the stochastic solution processes related to the nonlinear damped Duffing oscillator model which is
excited randomly by white noise process. Under the application of WHE, a deterministic model is
generated to simulate the statistical measures. In next stages, smi-analytical treatments are performed
under applying multi-step differential transformed method (Ms-DTM) and some cases study are illustrated
related to the statistical properties using Mathematica10 software.
Keywords
Wiener–Hermit expan- sion; Multi-step differential transformed method; Mathematica10; Stochastic nonlinear damped Duffing oscillator; Deterministic systems
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