The numerical solution of the point kinetics equation using the matrix exponential method

2013 ◽  
Vol 55 ◽  
pp. 42-48 ◽  
Author(s):  
Yujin Park ◽  
Kil To Chong
Keyword(s):  
Numerical Solution ◽  
Matrix Exponential ◽  
Kinetics Equation ◽  
The Matrix ◽  
Exponential Method ◽  
Point Kinetics

scholarly journals MATRIX EXPONENTIAL METHODS FOR PARALLEL COMPUTING OF ISOTOPIC DEPLETION AND SPECIES TRANSPORT FOR MOLTEN SALT REACTOR ANALYSIS

2021 ◽  
Vol 247 ◽  
pp. 06047
Author(s):  
Zack Taylor ◽  
Benjamin Collins ◽  
Ivan Maldonado
Keyword(s):  
Differential Equations ◽  
Molten Salt ◽  
Fission Products ◽  
Matrix Exponential ◽  
Fissile Material ◽  
Species Transport ◽  
The Matrix ◽  
Exponential Method ◽  
Reactor Loop ◽  
Exponential Methods

Matrix exponential methods have long been utilized for isotopic depletion in nuclear fuel calculations. In this paper we discuss the development of such methods in addition to species transport for liquid fueled molten salt reactors (MSRs). Conventional nuclear reactors work with fixed fuel assemblies in which fission products and fissile material do not transport throughout the core. Liquid fueled molten salt reactors work in a much different way, allowing for material to transport throughout the primary reactor loop. Because of this, fission product transport must be taken into account. The set of partial differential equations that apply are discretized into systems of first order ordinary differential equations (ODEs). The exact solution to the set of ODEs is herein being estimated using the matrix exponential method known as the Chebychev Rational Approximation Method (CRAM).

Relative error analysis of matrix exponential approximations for numerical integration

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Stefano Maset
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Numerical Solution ◽  
Relative Error ◽  
Absolute Error ◽  
Linear Ordinary Differential Equation ◽  
Matrix Exponential ◽  
Initial Value ◽  
The Matrix ◽  
Long Time

AbstractIn this paper, we study the relative error in the numerical solution of a linear ordinary differential equation y′(t) = Ay(t), t ≥ 0, where A is a normal matrix. The numerical solution is obtained by using at any step an approximation of the matrix exponential, e.g. a polynomial or a rational approximation. The error of the numerical solution with respect to the exact solution is due to this approximation as well as to a possible perturbation in the initial value. For an unperturbed initial value, we find: 1) unlike the absolute error, the relative error always grows linearly in time; 2) in the long-time, the contributions to the relative error relevant to non-rightmost eigenvalues of A disappear.

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