Numerical solution of stochastic nonlinear differential equations using Wiener-Hermite expansion

Al-Johani, Amna S.; El-Beltagy, Mohamed A.

doi:10.1063/1.4825950

Cited by 2 publications

(3 citation statements)

References 8 publications

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“…In the equation (13), by attention to the dimension of β and η 2 , it is clear that f (r) = 2η 2 n e (r) β − 1 is a dimensionless function of r. From the mathematical point of view, this is a nonlinear ordinary differential equation which is very similar to the Bessel ordinary differential equation. There are classic [21] and new [22][23][24][25][26][27][28] references about the nonlinear differential equations (partial and ordinary) in physics and mathematics. It is still a fascinating area for research on finding analytical solution, where be simple and general straightforward.…”

Section: Cylindrical Coordinatementioning

confidence: 99%

Analytical Solving a Nonlinear Model of the Glow Discharge

Aram¹

2022

PPT

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A nonlinear model has been introduced for the positive column of DC glow discharge in apure sealed, or low flow, gas media by including the diffusion, recombination, attachment, detachment,process and having the two-step ionization process of the metastable excited states, too. By thecombination of the system of the nonlinear continuity equations of the system, using some physicalestimations, and degrading the resulted nonlinear PDE in polar and rectangular systems of coordinatethe steady-state nonlinear ODE have been derived. Using a series-based solution, an innovativenonlinear recursion relation has been proposed for calculating the sentence of series. Using the stateof elimination of free charge on the outer boundary of the discharge vessel, the universal equation ofthe characteristic energy of the electrons versus the similarity variable, using the maximum degree ofionization as the parameter, has been derived.

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Section: Cylindrical Coordinatementioning

confidence: 99%

Analytical Solving a Nonlinear Model of the Glow Discharge

Aram¹

2022

PPT

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“…The first technique which will be discussed is the Weiner Hermite Expansion (WHE), this technique is helpful in converting the SDE associated with white noise to a system of deterministic equations solved either analytically or numerically [10], [16]. Any system involves white noise as an input can be written in a series of multiple Wiener integrals, therefore the system contains a sequence of Wiener kernels [11].…”

Section: Spectral Techniquesmentioning

confidence: 99%

“…The WHE takes the form is the mean and is the kth deterministic kernel of is the Gaussian term are the non-Gaussian terms. So, in order to solve any SDE, substituting by (2) in the SDE, after that projection on will be applied followed by taking ensemble average, calculating the statistical properties, such as the mean and the variance [10] The second technique to be considered in this paper is the polynomial chaos expansion (PCE), It provides orthogonal basis for the space of second-order random variables, this technique is used in models associated to random parameters with known probability distribution, where the stochastic quantities are uniquely identified in terms of their coordinates with respect to the basis [12]. To know PCE, two numbers must be selected, the first is the order that is considered as the highest power and the second is the dimension that is known from the number of used basis.…”

Section: Spectral Techniquesmentioning

confidence: 99%

Study of Stochastic Spread-out of Virus Model Associated with Random parameters

Hashem

El-Beltagy

El-Dewaik

2020

2020 2nd Novel Intelligent and Leading Emerging Sciences Conference (NILES)

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The spread-out of viruses has a great impact on people all over the world. Solving deterministic population models can be useful in understanding the changes results from spreading of virus, these models can be complicated if they are associated with any stochastic random parameters. In the current work, simulation and prediction of the virus behavior will be obtained by using spectral techniques. The stochastic models may be associated with more than one source of randomness, it might be noise or random coefficients or both. Spectral techniques are more efficient than other techniques in solving the stochastic models, for example, Wiener Hermite expansion technique, this technique is used to solve the models associated with noise resulting from different sources. It is helpful in predicting and simulating the behavior of the virus, one of the advantages is having high order of convergence. The statistical properties such as the expectation and the variance are calculated and compared with other techniques.

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Numerical solution of stochastic nonlinear differential equations using Wiener-Hermite expansion

Cited by 2 publications

References 8 publications

Analytical Solving a Nonlinear Model of the Glow Discharge

Analytical Solving a Nonlinear Model of the Glow Discharge

Study of Stochastic Spread-out of Virus Model Associated with Random parameters

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