The Homotopy Wiener-Hermite Expansion and Perturbation Technique (WHEP)

2008 ◽  
pp. 159-180 ◽  
Author(s):  
Magdy A. El-Tawil
Keyword(s):  
Perturbation Technique ◽  
Hermite Expansion

scholarly journals Solution of the Stochastic Heat Equation with Nonlinear Losses Using Wiener-Hermite Expansion

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Mohamed A. El-Beltagy ◽  
Noha A. Al-Mulla
Keyword(s):  
Heat Equation ◽  
Perturbation Technique ◽  
Stochastic Heat Equation ◽  
Nonlinear Pdes ◽  
Deterministic System ◽  
Hermite Expansion ◽  
Expansion Technique ◽  
Stochastic Solution ◽  
The Stochastic Heat Equation ◽  
Non Gaussian

In the current work, the Wiener-Hermite expansion (WHE) is used to solve the stochastic heat equation with nonlinear losses. WHE is used to deduce the equivalent deterministic system up to third order accuracy. The solution of the equivalent deterministic system is obtained using different techniques numerically and analytically. The finite-volume method (FVM) with Pickard iteration is used to solve the equivalent system iteratively. The WHE with perturbation technique (WHEP) is applied to deduce more simple and decoupled equivalent deterministic system that can be solved numerically without iterations. The system resulting from WHEP technique is solved also analytically using the eigenfunction expansion technique. The Monte-Carlo simulations (MCS) are performed to get the statistical properties of the stochastic solution and to verify other solution techniques. The results show that higher-order solutions are essential especially in case of nonlinearities where non-Gaussian effects cannot be neglected. The comparisons show the efficiency of the numerical WHE and WHEP techniques in solving stochastic nonlinear PDEs compared with the analytical solution and MCS.

Usefulness of Foundry Tooling Materials in Microwave Heating Process

2013 ◽  
Vol 58 (3) ◽  
pp. 919-922 ◽  
Author(s):  
K. Granat ◽  
B. Opyd ◽  
D. Nowak ◽  
M. Stachowicz ◽  
G. Jaworski
Keyword(s):  
Electromagnetic Field ◽  
Microwave Heating ◽  
Loss Factor ◽  
Perturbation Technique ◽  
Resonant Cavity ◽  
Precise Determination ◽  
Heating Process ◽  
Basic Criterion ◽  
Measurement Results ◽  
Heating Technology

Abstract The paper describes preliminary examinations on establishing usefulness criteria of foundry tooling materials in the microwave heating technology. Presented are measurement results of permittivity and loss tangent that determine behaviour of the materials in electromagnetic field. The measurements were carried-out in a waveguide resonant cavity that permits precise determination the above-mentioned parameters by perturbation technique. Examined were five different materials designed for use in foundry tooling. Determined was the loss factor that permits evaluating usefulness of materials in microwave heating technology. It was demonstrated that the selected plastics meet the basic criterion that is transparency for electromagnetic radiation.

Slip And Hall Effects On The Flow Of A Hyperbolic Tangent Fluid Through Porous Medium In A Planar Channel With Peristalsis

GIS Business ◽  
2020 ◽  
Vol 15 (1) ◽  
pp. 383-394
Author(s):  
K. Shalini ◽  
K.Rajasekhar
Keyword(s):  
Porous Medium ◽  
Pressure Gradient ◽  
Volume Flow Rate ◽  
Perturbation Technique ◽  
Volume Flow ◽  
Planar Channel ◽  
Hyperbolic Tangent ◽  
Closed Form Solutions ◽  
Long Wavelength ◽  
Hall Effects

In this paper, the effect of Slip and Hall effects on the flow of Hyperbolic tangent fluid through a porous medium in a planar channel with peristalsis under the assumption of long wavelength is investigated. A Closed form solutions are obtained for axial velocity and pressure gradient by employing perturbation technique. The effects of various emerging parameters on the pressure gradient, time averaged volume flow rate and frictional force are discussed with the aid of graphs.

scholarly journals Approximate Analytical Solution of Nonlinear Evolution Equations

2020 ◽  
Author(s):  
Laxmikanta Mandi ◽  
Kaushik Roy ◽  
Prasanta Chatterjee
Keyword(s):  
Acoustic Waves ◽  
Evolution Equations ◽  
Solitary Wave Solution ◽  
Perturbation Technique ◽  
Nonlinear Evolution Equations ◽  
Charged Dust ◽  
De Vries ◽  
Frame Work ◽  
Dust Grain ◽  
Charged Ions

Analytical solitary wave solution of the dust ion acoustic waves (DIAWs) is studied in the frame-work of Korteweg-de Vries (KdV), damped force Korteweg-de Vries (DFKdV), damped force modified Korteweg-de Vries (DFMKdV) and damped forced Zakharov-Kuznetsov (DFZK) equations in an unmagnetized collisional dusty plasma consisting of negatively charged dust grain, positively charged ions, Maxwellian distributed electrons and neutral particles. Using reductive perturbation technique (RPT), the evolution equations are obtained for DIAWs.

scholarly journals A modified Tikhonov regularization method based on Hermite expansion for solving the Cauchy problem of the Laplace equation

2020 ◽  
Vol 18 (1) ◽  
pp. 1685-1697
Author(s):  
Zhenyu Zhao ◽  
Lei You ◽  
Zehong Meng
Keyword(s):  
Cauchy Problem ◽  
Laplace Equation ◽  
Tikhonov Regularization ◽  
Regularization Method ◽  
Regularization Parameter ◽  
Solution Process ◽  
Tikhonov Regularization Method ◽  
Hermite Expansion ◽  
The Cauchy Problem ◽  
Ill Posed

Abstract In this paper, a Cauchy problem for the Laplace equation is considered. We develop a modified Tikhonov regularization method based on Hermite expansion to deal with the ill posed-ness of the problem. The regularization parameter is determined by a discrepancy principle. For various smoothness conditions, the solution process of the method is uniform and the convergence rate can be obtained self-adaptively. Numerical tests are also carried out to verify the effectiveness of the method.

scholarly journals The Effect of Wall Shear Stress on Two Phase Fluctuating Flow of Dusty Fluids by Using Light Hill Technique

Water ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 1587
Author(s):  
Dolat Khan ◽  
Ata ur Rahman ◽  
Gohar Ali ◽  
Poom Kumam ◽  
Attapol Kaewkhao ◽  
...  
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
Base Fluid ◽  
Perturbation Technique ◽  
Fluid Velocity ◽  
Dust Particles ◽  
Stress Effect ◽  
Parallel Plates ◽  
Dusty Fluid ◽  
Wall Shear

Due to the importance of wall shear stress effect and dust fluid in daily life fluid problems. This paper aims to discover the influence of wall shear stress on dust fluids of fluctuating flow. The flow is considered between two parallel plates that are non-conducting. Due to the transformation of heat, the fluid flow is generated. We consider every dust particle having spherical uniformly disperse in the base fluid. The perturb solution is obtained by applying the Poincare-Lighthill perturbation technique (PLPT). The fluid velocity and shear stress are discussed for the different parameters like Grashof number, magnetic parameter, radiation parameter, and dusty fluid parameter. Graphical results for fluid and dust particles are plotted through Mathcad-15. The behavior of base fluid and dusty fluid is matching for different embedded parameters.

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