Abstract
Since 2004, SCKCEN has been engaged in the development of the ALEPH code. The ALEPH code is used to determine the behaviour of nuclear reactor cores. In this code, two equations are important, namely the neutron transport equations and the Bateman equations. The neutron transport equations determine the
neutron ux and the Bateman equations are used to describe the time evolution of the nuclide concentrations. The transport equations can be solved using stochastic methods, such as the Monte Carlo algorithms. In general, Monte Carlo methods can be used to look for numerical solutions equations with a probabilistic interpretation. A way of implementing Monte Carlo methods is through Monte Carlo Nparticle code. The objective of this master thesis is to improve the way the Bateman equations are currently worked out. The
Bateman equations will be solved with deterministic methods. This master thesis is organized as follows. First, the Bateman equations with their properties will be described. Thereafter, the different algorithms which could possibly be used to solve the Bateman equations, will be discussed. These algorithms are
 Calculating the exponential of the system matrix using the scaling and squaring algorithm
 Chebyshev Rational Approximation method
 RadauIIA method.
Finally, it will be examined which is the best algorithm to solve the Bateman equations.
neutron ux and the Bateman equations are used to describe the time evolution of the nuclide concentrations. The transport equations can be solved using stochastic methods, such as the Monte Carlo algorithms. In general, Monte Carlo methods can be used to look for numerical solutions equations with a probabilistic interpretation. A way of implementing Monte Carlo methods is through Monte Carlo Nparticle code. The objective of this master thesis is to improve the way the Bateman equations are currently worked out. The
Bateman equations will be solved with deterministic methods. This master thesis is organized as follows. First, the Bateman equations with their properties will be described. Thereafter, the different algorithms which could possibly be used to solve the Bateman equations, will be discussed. These algorithms are
 Calculating the exponential of the system matrix using the scaling and squaring algorithm
 Chebyshev Rational Approximation method
 RadauIIA method.
Finally, it will be examined which is the best algorithm to solve the Bateman equations.
Original language  English 

Qualification  Master of Science 
Awarding Institution 

Supervisors/Advisors 

State  Published  2016 