Open AccessA refined way of solving reactor point kinetics equations for imposed reactivity insertions
Author(s) -
B. D. Ganapol
Publication year - 2009
Publication title -
nuclear technology and radiation protection
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.31
H-Index - 16
eISSN - 1452-8185
pISSN - 1451-3994
DOI - 10.2298/ntrp0903157g
Subject(s) - extrapolation , simplicity , convergence (economics) , acceleration , variety (cybernetics) , mathematics , reactivity (psychology) , term (time) , computer science , point (geometry) , feature (linguistics) , simple (philosophy) , richardson extrapolation , algorithm , mathematical analysis , physics , classical mechanics , geometry , artificial intelligence , medicine , linguistics , philosophy , alternative medicine , epistemology , quantum mechanics , pathology , economics , economic growth
We apply the concept of convergence acceleration, also known as extrapolation, to find the solution of the reactor kinetics equations (RKEs). The method features simplicity in that an approximate finite difference formulation is constructed and converged to high accuracy from knowledge of the error term. Through the Romberg extrapolation, we demonstrate its high accuracy for a variety of imposed reactivity insertions found in the literature. The unique feature of the proposed algorithm, called RKE/R(omberg), is that no special attention is given to the stiffness of the RKEs. Finally, because of its simplicity and accuracy, the RKE/R algorithm is arguably the most efficient numerical solution of the RKEs developed to date