scholarly journals Solution for the Multigroup Neutron Space Kinetics Equations by Source Iterative Method

2021 ◽  
Vol 9 (2A) ◽  
Author(s):  
Matheus Gularte Tavares
Keyword(s):  
Laplace Transform ◽  
Neutron Flux ◽  
Source Term ◽  
Polynomial Interpolation ◽  
Initial Guess ◽  
Inverse Laplace Transform ◽  
Numerical Inverse Laplace Transform ◽  
Laplace Transform Technique ◽  
Linear Differential ◽  
Multigroup Neutron

In this work, we used a modified Picard’s method to solve the Multigroup Neutron Space Kinetics Equations (MNSKE) in Cartesian geometry. The method consists in assuming an initial guess for the neutron flux and using it to calculate a fictitious source term in the MNSKE. A new source term is calculated applying its solution, and so on, iteratively, until a stop criterion is satisfied. For the solution of the fast and thermal neutron fluxes equations, the Laplace Transform technique is used in time variable resulting in a first order linear differential matrix equation, which are solved by classical methods in the literature. After each iteration, the scalar neutron flux and the delayed neutron precursors are reconstructed by polynomial interpolation. We obtain the fluxes and precursors through Numerical Inverse Laplace Transform by Stehfest method. We present numerical simulations and comparisons with available results in literature.

scholarly journals Quadrature Integration Techniques for Random Hyperbolic PDE Problems

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 160
Author(s):  
Rafael Company ◽  
Vera N. Egorova ◽  
Lucas Jódar
Keyword(s):  
Numerical Methods ◽  
Laplace Transform ◽  
Quadrature Rule ◽  
Inverse Laplace Transform ◽  
Process Time ◽  
Efficient Computation ◽  
Hyperbolic Pde ◽  
Numerical Convergence ◽  
Laplace Transform Technique ◽  
Integration Techniques

In this paper, we consider random hyperbolic partial differential equation (PDE) problems following the mean square approach and Laplace transform technique. Randomness requires not only the computation of the approximating stochastic processes, but also its statistical moments. Hence, appropriate numerical methods should allow for the efficient computation of the expectation and variance. Here, we analyse different numerical methods around the inverse Laplace transform and its evaluation by using several integration techniques, including midpoint quadrature rule, Gauss–Laguerre quadrature and its extensions, and the Talbot algorithm. Simulations, numerical convergence, and computational process time with experiments are shown.

Numerical Inversion of Laplace Transform for Time Resolved Thermal Characterization Experiment

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
J. Toutain ◽  
J.-L. Battaglia ◽  
C. Pradere ◽  
J. Pailhes ◽  
A. Kusiak ◽  
...  
Keyword(s):  
Fourier Series ◽  
Laplace Transform ◽  
Periodic Function ◽  
Thermal Characterization ◽  
Inverse Laplace Transform ◽  
Numerical Inversion ◽  
Time Resolved ◽  
Reliable Technique ◽  
Numerical Inverse Laplace Transform ◽  
Thermal Disturbance

The aim of this technical brief is to test numerical inverse Laplace transform methods with application in the framework of the thermal characterization experiment. The objective is to find the most reliable technique in the case of a time resolved experiment based on a thermal disturbance in the form of a periodic function or a distribution. The reliability of methods based on the Fourier series methods is demonstrated.

Unsteady Hydromagnetic Radiative Flow of a Dusty Fluid Past a Porous Plate With Ramped Wall Temperature

2013 ◽  
Author(s):  
R. Nandkeolyar ◽  
P. Sibanda ◽  
Md. S. Ansari
Keyword(s):  
Magnetic Field ◽  
Laplace Transform ◽  
Porous Plate ◽  
Inverse Laplace Transform ◽  
Combined Effects ◽  
Dusty Fluid ◽  
Electrically Conducting ◽  
Flow Parameters ◽  
Energy Transfers ◽  
Laplace Transform Technique

The combined effects of applied magnetic field, thermal radiation and suction on the flow and free convective heat transfer of a viscous, incompressible, electrically conducting dusty fluid past a flat plate with ramped temperature are studied. The governing partial differential equations for momentum and energy transfers, for both the fluid and particle phases, are solved using Laplace transform technique. The inverse Laplace transform is obtained numerically using Matlab. A comparison of Numerical solution and analytical solution for energy transfer is made which shows an excellent agreement. The effects of pertinent flow parameters are analyzed with the help of graphs and tables.

Stability analysis of fractional-order systems with double noncommensurate orders for matrix case

2011 ◽  
Vol 14 (3) ◽  
Author(s):  
Zhuang Jiao ◽  
YangQuan Chen
Keyword(s):  
Fractional Order ◽  
Linear Time ◽  
Simple Algorithm ◽  
Inverse Laplace Transform ◽  
Order System ◽  
Necessary Condition ◽  
Fractional Order Systems ◽  
Numerical Inverse Laplace Transform ◽  
Laplace Transform Technique ◽  
Matrix Case

AbstractBounded-input bounded-output stability issues for fractional-order linear time invariant (LTI) system with double noncommensurate orders for the matrix case have been established in this paper. Sufficient and necessary condition of stability is given, and a simple algorithm to test the stability for this kind of fractional-order systems is presented. Based on the numerical inverse Laplace transform technique, time-domain responses for fractional-order system with double noncommensurate orders are shown in numerical examples to illustrate the proposed results.

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