Numerical Simulation Using Haar Wavelet Operational Method for Neutron Point Kinetic Equation Involving Imposed Reactivity Function

2015 ◽  
pp. 180-195
Keyword(s):  
Numerical Simulation ◽  
Kinetic Equation ◽  
Haar Wavelet ◽  
Operational Method

scholarly journals Numerical Solution of Fractional Electrical Circuits by Haar Wavelet

MATEMATIKA ◽  
2019 ◽  
Vol 35 (3) ◽  
Author(s):  
Sahar Altaf Ahmed ◽  
Sumaira Yousuf Khan
Keyword(s):  
Numerical Simulation ◽  
Comparative Analysis ◽  
Numerical Solution ◽  
Numerical Scheme ◽  
Numerical Approximation ◽  
Time Derivative ◽  
Haar Wavelet ◽  
Electrical Circuits ◽  
Fractional Time Derivative

In this study, numerical approximation of electrical circuits in terms of Caputo fractional time derivative was examined. The order of the derivative being considered was. Haar Wavelet numerical scheme was used to derive the solutions of the fractional electrical circuits, namely RC, LC and RLC. The comparative analysis of numerical simulation of each equation with the classical ones was also provided.

Quasilinearized Scale-3 Haar wavelets-based algorithm for numerical simulation of fractional dynamical systems

2018 ◽  
Vol 35 (5) ◽  
pp. 1907-1931 ◽  
Author(s):  
R.C. Mittal ◽  
Sapna Pandit
Keyword(s):  
Dynamical System ◽  
Numerical Simulation ◽  
Haar Wavelet ◽  
Haar Wavelets ◽  
Content Type ◽  
System A ◽  
Resolution Level ◽  
Gauss Elimination ◽  
First Time ◽  
Fractional Dynamical System

Purpose The main purpose of this work is to develop a novel algorithm based on Scale-3 Haar wavelets (S-3 HW) and quasilinearization for numerical simulation of dynamical system of ordinary differential equations. Design/methodology/approach The first step in the development of the algorithm is quasilinearization process to linearize the problem, and then Scale-3 Haar wavelets are used for space discretization. Finally, the obtained system is solved by Gauss elimination method. Findings Some numerical examples of fractional dynamical system are considered to check the accuracy of the algorithm. Numerical results show that quasilinearization with Scale-3 Haar wavelet converges fast even for small number of collocation points as compared of classical Scale-2 Haar wavelet (S-2 HW) method. The convergence analysis of the proposed algorithm has been shown that as we increase the resolution level of Scale-3 Haar wavelet error goes to zero rapidly. Originality/value To the best of authors’ knowledge, this is the first time that new Haar wavelets Scale-3 have been used in fractional system. A new scheme is developed for dynamical system based on new Scale-3 Haar wavelets. These wavelets take less time than Scale-2 Haar wavelets. This approach extends the idea of Jiwari (2015, 2012) via translation and dilation of Haar function at Scale-3.

scholarly journals Evaluation of a spectral line width for the Phillips spectrum by means of numerical simulation

2015 ◽  
Vol 22 (3) ◽  
pp. 325-335 ◽  
Author(s):  
A. O. Korotkevich ◽  
V. E. Zakharov
Keyword(s):  
Numerical Simulation ◽  
Kinetic Equation ◽  
Spectral Line ◽  
Line Width ◽  
Water Waves ◽  
Spectral Lines ◽  
Dynamical Equations ◽  
Spectral Line Width ◽  
Original Motivation ◽  
Different Levels

Abstract. The work aims to check one of the assumptions under which the kinetic equation for water waves was derived in order to understand whether it can be applied to the situations described by the Phillips spectrum. We evaluate a spectral line width of the spectrum from the simulations in the framework of primordial dynamical equations at different levels of nonlinearity in the system, corresponding to the weakly turbulent Kolmogorov–Zakharov spectra ω−4, Phillips spectra ω−5, and intermediate cases. The original motivation of the work was to check one of the assumptions under which the kinetic equation for water waves was derived in order to understand whether it can be applied to the Phillips spectrum. It is shown that, even in the case of relatively high average steepness, when the Phillips spectrum is present in the system, the spectral lines are still very narrow, at least in the region of the direct cascade spectrum. It allows us to state that, even in the case of the Phillips spectrum, one of the assumptions used for the derivation of the Hasselmann kinetic equation is still valid, at least in the case of moderate whitecapping.

Numerical Simulation Analysis of Dynamic Parameters of the Vibratory Sinking Piling System

2012 ◽  
Vol 170-173 ◽  
pp. 661-665
Author(s):  
Xiao Peng Li ◽  
Xiao Chen Meng ◽  
Wei Wang ◽  
Mi Que Zhao
Keyword(s):  
Numerical Simulation ◽  
Kinetic Equation ◽  
Dynamic Optimization ◽  
Theoretical Basis ◽  
Analytic Solution ◽  
Simulation Analysis ◽  
Work Efficiency ◽  
Soil System ◽  
Mechanics Model ◽  
The Relationship

In the premise of mechanics model and the kinetic equation, the numerical simulation model of pile-soil system has been established with MATLAB, and the numerical analytic solution of kinetic equation has been got by fourth-order Runge-Kutta. And the relationship curves between the pile-soil interface’s friction and time, displacement, acceleration and velocity of the pile have been mainly studied when the exciting amplitude is 100kN, 200kN respectively. With the work, the exciting amplitude will be obtained. In this way, the friction of the pile-soil can be decreased and work efficiency can be improved; besides this paper can also provide a further theoretical basis of pile pressing machine's dynamic optimization.

Water uptake by substituted amylose tablets: experimentation and numerical simulation

2009 ◽  
Vol 00 (00) ◽  
pp. 090904073309027-8
Author(s):  
H.W. Wang ◽  
S. Kyriacos ◽  
L. Cartilier
Keyword(s):  
Numerical Simulation ◽  
Water Uptake
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